This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Main emphasis is on the differential and integral calculus of functions of a single variable. The systems of real and complex numbers. Least upper bound and greatest lower bound. Natural numbers and induction. Mappings and functions. Sequences and limits. Series and convergence tests. Conditionally convergent series. Limits and continuous functions. Trigonometric functions. Differentiation. Extreme values. The mean value theorem and polynomial approximation. Integration. The fundamental theorem of calculus. Logarithmic and exponential functions, hyperbolic and inverse trigonometric functions. Methods for finding antiderivatives. Real power series. First-order differential equations. Complex valued functions and second-order differential equations.

Introduce students to methods and fundamental laws of mechanics, waves and thermodynamics, to the extent that they can apply their knowledge to solve problems. 

Concepts, units, scales and dimensions.  Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body.  Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound.  Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics.

Note that the textbook is accessible to students via Canvas free of charge.

There are 4 lab sessions with experiments mainly from mechanics, with emphasis on teaching students methods of data collection and data processing. Student hand in a lab report on each experiment. They also hand in a final report from one of these that is intended to look more like a journal article.

The course emphasizes geological processes as a consequence of endogenic processes.

Main topics covered in the course:

• The main features of the Earth’s internal structure, with emphasis on its layering and the properties of individual layers.
• Early hypotheses about continental drift and their development leading to plate tectonics theory, with emphasis on why and how the relative positions of plates and continents are constantly changing.
• The fundamentals of mineral and rock formation and metamorphism.
• Volcanism: causes, distribution, and hazards, with special reference to Iceland.
• Causes of earthquakes and their distribution, different types and behavior of seismic waves, and how this knowledge can be used, for example, to locate and assess the size of earthquakes.
• Structural geology: faults, folds, mountain building, and associated forces.
• Geological time and dating methods, and the geologic time scale, i.e., the arrangement of strata in time and space.
• In addition to general discussion of the course content, special emphasis is placed on the geological and geohistorical formation and position of Iceland.

Teaching Arrangement

The course is 7.5 ECTS and spans 14 weeks. Course content is presented in lectures, selected reading material, practical exercises, and three field trips.

• Lectures are tvice a week inaddtion to on excercise class.
• Field trips: Day trips, usually during the first 4–5 weeks of the semester. Attendance is mandatory. Note field trips can be on weekends.
• Practical exercises: Conducted in classrooms and around the University. Attendance is mandatory.
• Chapter quizzes: Weekly multiple-choice quizzes on textbook chapters. Each quiz is 10 minutes, taken at the beginning of Monday lectures, linked to individual chapters.

Assessment

Assessment is threefold, and all components must be passed with a minimum grade of 5 to pass the course.

• In class exams: 20%
• Field trips and practical exercises: 30%
• Written final exam: 50%

Required Texts and Materials

• Earth – Portrait of a Planet (required). Second half of the book is used in JAR202G.
• Geological Field Techniques (required – pdf provided).
• Compass with clinometer (required).
• Good field notebook (required).
• Hammer, hand lens (recommended).

Teaching Statement

To succeed in this course, students must actively participate in lectures and assignments. Knowledge is gained through lectures and readings, but assignments and field trips are essential to deepen understanding and practice methods. Teachers will make key concepts and materials accessible, but students are expected to learn independently and ask questions if unclear. Teachers emphasize participation in course evaluations to address improvements. The midterm survey will be reviewed with students after completion.

Code of Conduct

Great emphasis is placed on honest academic work in accordance with the University of Iceland’s Code of Ethics:
https://www.hi.is/haskolinn/sidareglur
If a student is found guilty of misconduct in exams or coursework, action will be taken as outlined in the University’s regulations:
https://ugla.hi.is/kennsluskra/index.php?tab=skoli&chapter=content&id=46779

Turnitin

Assignments in this course will be checked using Turnitin.

Artificial Intelligence

Use of AI in studies at the University of Iceland is governed by university guidelines:
https://gervigreind.hi.is/
In this course, the use of AI in assignments and/or exams is not permitted unless explicitly allowed by the instructors. Any uncertainty regarding AI use must be clarified with the course coordinator.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Tutor classes for Earth Science students

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Emphasis is laid on the theoretical aspects of the material. The aim is that the students acquire understanding of fundamental concepts and are able to use them, both in theoretical consideration and in calculations. Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobian matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flows. Cylindrical and spherical coordinates. Taylor polynomials. Extrema and classification of stationary points. Extrema with constraints. Implicit functions and local inverses. Line integrals and potential functions. Proper and improper multiple integrals. Change of variables in multiple integrals. Simply connected regions. Integration on surfaces. Theorems of Green, Stokes and Gauss.

Introduction to electrodynamics in material; from insulators to superconductors.  Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics.

There are four 4 hour lab sessions and two 3 hour sessions, from optics and electromagnetism. Students hand in a lab report on each experiment. They also hand in a final report from one of the 4 hour experiments that is intended to look more like a journal article.

This course focuses on the Earth Surface processes, specifically those that contribute to the formation of various landforms and landscapes and how these landforms evolve and erode over time and space. Emphasis is placed on enabling students to discuss these geological processes using geological terminology in both Icelandic and English.

Key topics include:

• Basic sedimentology, with a focus on changes in grain size, distribution, and texture of rock particles during transport by running water, glaciers, and wind.
• Earth's water cycle and its significant role in shaping terrestrial landscapes through weathering, erosion, and deposition of rock material.
• Running water as the most influential agent in shaping Earth's land surfaces through both erosion and transport of rock debris.
• Coastal dynamics and factors influencing shoreline development, highlighting the ongoing changes, fast and slow, at the land-sea boundary.
• Groundwater's role in land formation, its importance for drinking water supply, and measures to protect this vital resource.
• The Earth's atmospheric circulation, its influence on precipitation patterns, and the distribution of arid and vegetative areas.
• Erosional and depositional processes and their role in landform development in Iceland, focusing on glaciation and its history, especially during the last ice age.
• Discussion of Earth's inorganic and organic resources, their formation, distribution, extraction, usage, disposal, renewal, and recycling.
• Special emphasis is placed on relating the theoretical aspects of the course to Iceland by exploring relevant local examples.

Teaching Arrangement

The course is worth 7.5 ECTS and spans 14 weeks. Material is presented through lectures, selected readings, and a 5-day field trip to South Iceland and the Westman Islands. The primary purpose of the field trip is to provide students with direct experience of the processes and landforms covered in the course. The field trip takes place immediately after the spring exams and is mandatory. Students must cover their own meal expenses during the trip. Weekly multiple-choice exams related to textbook chapters are assigned.

Teaching Statement

For students to succeed in this course, active participation in lectures and assignments is key. Students will gain knowledge through lectures and reading material but completing assignments and attending field trips are essential for deepening understanding of key concepts and methods. Instructors will make course concepts accessible, but students are expected to learn independently and ask questions if anything is unclear. Instructors emphasize the importance of student feedback through course evaluations to address areas for improvement, with a mid-term evaluation reviewed with students.

Assessment

The course assessment is three-fold, and all parts must be completed with a minimum grade of 5 to pass the course.

• Multiple choice exams: 25%

• Field trip journal: 15%
• Written final exam: 60%

Learning Outcomes:

Upon completing the course, students should be able to:

• Use geological terminology to discuss the natural environment of the land.
• Explain the role of Earth's exogenic forces in the ever-changing appearance of its land surface.
• Provide examples of how the effects of these exogenic forces vary across time and space.
• Analyze the role of exogenic forces in shaping individual landforms and landscapes.
• Identify individual landforms and landscapes and link them to one or more exogenic processes.
• Analyze composite evidence of exogenic processes and use that analysis to describe the sequence of events, in time and space, that created specific landforms and landscapes.
• Read geological maps that show surface deposits.
• Record and manage their own observations in a field notebook.

An introduction to the physics of the Earth. Origin and age of the Earth. Dating with radioactive elements. Gravity, shape and rotation of the Earth, the geomagnetic field, magnetic anomalies, palaeomagnetism, electric conductivity. Earthquakes, seismograph and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Geophysical research in Iceland.

Practicals include solving problems set for each week and exercises in the use of geophysical instruments.  Students write one essay on a selected topic in geophysics.

Basic principles and mathematical methods in thermodynamics,laws of thermodynamics, state functions, Maxwell relations, equilibrium, phase transitions, quantum statistical mechanics, ideal and real gases, specific heat, rate theory, Bose and Fermi distributions.

The objective of the course is to teach the student the basic concepts of thermodynamic systems. The students should also understand different forms of energy, energy transport and conversion from one state to another. The student should be able to calculate the rates of chemical reactions and energy balance.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

Programming in Python (for computations in engineering and science): Main commands and statements (computations, control statements, in- and output), definition and execution of functions, datatypes (numbers, matrices, strings, logical values, records), operations and built-in functions, array and matrix computation, file processing, statistics, graphics. Object-oriented programming: classes, objects, constructors and methods. Concepts associated with design and construction of program systems: Programming environment and practices, design and documentation of function and subroutine libraries, debugging and testing of programmes.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

The course is aimed at students that have already taken a first course in geophysics and have basic knowledge of geophysical exploration and its application.  The course is split in two parts:

1. a) Four to five days of field work at the beginning of autumn term.  Several geophysical methods applied to practical problems.
2. b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computation excises and model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Goal: To teach students the properties of electronic components and circuits, measurement technologies and train them in methods and solutions for electronic circuit design, measurements, research and data acquisition. 

Curriculum: The course covers fundamental issues in electronics, the physics of electronics and electronic components and measurement technology. The curriculum includes theory and practical analysis of AC and dc circuits, diodes and transistors, operational amplifiers and feedback, logic components and digital circuits, digital measurement techniques, amplification and filtering. The course includes twelve laboratory sessions and a project on a microcomputer controlled measurement system. The course concludes with a written exam.

The equations of Laplace and Poisson. Magnetostatics. Induction.  Maxwell's equations. Energy of the electromagnetic field. Poynting's theorem. Electromagnetic waves. Plane waves in dielectric and conducting media, reflection and refraction.  Electromagnetic radiation and scattering. Damping.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

Basic concepts of thermodynamic systems, the zeroth law of thermodynamics. Work, internal energy, heat, enthalpy, the first law of thermodynamics for closed and open systems. Ideal and real gases, equations of state. The second law of thermodynamics, entropy, available energy. Thermodynamic cycles and heat engines, cooling engines and heat pumps. Thermodynamic potentials, Maxwell relations. Mixture of ideal gases. Properties for water and steam. Chemical potentials, chemical reactions of ideal gases, the third law of thermodynamics.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Geological and environmental history of the Earth from the Precambrian, Palaeozoic, Mesozoic, and Cenozoic to present. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, Wilson Cycle, climate history and evolution of life. Fossils, basic principles of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Icehouse and greenhouse Earth and climate change in general. The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the location that will eventually become Iceland. Gradual climate cooling during Cenozoic and implications. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Objectives:   To introduce continuum mechanics, fluid dynamics and heat transfer and their application to problems in physics and geophysics. I. Stress and strain, stress fields, stress tensor, bending of plates, models of material behaviour: elastic, viscous, plastic materials. II. Fluids, viscous fluids, laminar and turbulent flow, equation of continuity, Navier-Stokes equation. III. Heat transfer: Heat conduction, convection, advection and geothermal resources. Examples and problems from various branches of physics will be studied, particularly from geophysics.

Teaching statement: To do well in this course, students should actively participate in the discussions, attend lectures, give student presentations and deliver the problem sets assigned in the course. Students will gain knowledge through the lectures, but it is necessary to do the exercises to understand and train the use of the concepts. The exercises are intergrated in the text of the book, it is recommended to do them while reading the text. Instructors will strive to make the concepts and terminology accessible, but it is expected that students study independently and ask questions if something is unclear. In order to improve the course and its content, it is appreciated that students participate in the course evaluation, both the mid-term and the end of term course evaluation.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

The aim is to introduce students to the disciplines of general oceanography, in particular marine geological, physical and chemical oceanography. To understand how the interactions of processes shape the characteristics of different ocean regions.
The course covers the distribution of land and water, the world oceans and their geomorphology. Instruments and techniques in oceanographic observations. Physical properties of sea water. Energy and water budgets. Distribution of properties in relation to turbulence and diffusion. Introductory dynamical oceanography. Chemical oceanography: Geochemical balance, major and minor elements, dissolved gases. Biogeochemical cycles. Biological processes in relation to the physical and chemical environment. Oceanography of the North Atlantic and Icelandic waters

Students work on the BS-project under the supervision of a teacher.

Geological history of the Precambrian, Palaeozoic and Mesozoic. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, climate history and evolution of life. Fossils and stratigraphy, basic priciples of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Practical work: Written exercises, seminars and reports. Students give seminars and write reports on selected subjects.

Tectonic motions control the nature of the planet we inhabit and the location of continents, mountain ranges, volcanoes, where earthquakes occur and even are important for controlling the Earth's climate. Structural geology and crustal movements in the world, with special emphasis on movements in Iceland. This course introduces the techniques of structural geology through a survey of the mechanics of rock deformation, a survey of the features and geometries of faults and folds, and techniques of strain analysis. Regional structural geology and tectonics are introduced. The subject of the course is active tectonic movements and how this is manifested and recorded in the geological record with emphasis on processes currently active in Iceland. Lectures will be complimented with fieldwork and supportive examples will be given from a global perspective (e.g. compressional tectonics from the Andes and other extensional environments like the East Africa Rift). Methods to describe these processes will be taught and evaluated. Structural geology concepts including elastic, ductile, and brittle behavior of rocks in the crust and mantle will be discussed and discontinuities and brittle fracturing will be addressed. Plate tectonics, plate velocity models, both relative and absolute. Earthquakes. Plate boundary deformation including strike-slip, extensional, and compressive regimes with rifts and rifting structures and folds in addition to mountain building. (If time permits: microstructures, post-rifting and post-seismic movements, Isostasy, vertical crustal movements and sea level, and structural level. measuring crustal movements, GPS-geodesy, levelling, and analysis of seismic stratigraphy (i.e. active source seismic reflection and refraction profiles). Fieldwork will focus on discontinuity analysis and characterisation through a combination of exposure mapping with structural observations coupled with digital elevation (DEMs) model collection using drones and associated analysis to create a coherent assessment of active faults in Southwestern Iceland. Lectures are required as content in the lectures will be tested. Students visiting from abroad in Geology and Geophysics are encouraged to participate in this class as this will be held in English and provide excellent insight into the Iceland Tectonic and Plate Boundary system. 

The aim of the course is to give a comprehensive summary of the environmental change that occurred during the Quaternary period with special reference to Iceland. Contents: The characteristics of the Quaternary and geological evidence for global climatic change. Variations of Earth´s orbital parameters. Dating methods. Glacial debris transport and glacial sedimentation on land and in water. Evidence for climate change in glacier ice and marine and lake sediment. Volcanic activity and the environment. Paleoclimate reconstruction. The glacial and climatic history of Iceland and the North Atlantic Ocean. Grading: Final project 35%, assignments during the semester 30%, presentations 15%, Take home exam 20%. Part of the term project will be a comprehensive search for references to be used by students as they write their term paper and prepare a presentation to be given in class.

Heat budget of the Earth, heat transport to the Earth´s surface. Geothermal systems and their structure, renewability of geothermal systems, methodology in geothermal development, estimation of resource size, fluid origin and chemistry, water-rock interaction, environmental impact of utilization, well testing and well data integration.  The course is taught during 7-week period in the first part of the fall semester.  It consists of lectures, practical, student lectures, student posters, essay and exams.  The course is taught in English.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

The course will focus on the study of sediments and sedimentary rocks, erosion, transport processes and accumulation of sediments, and sedimentary facies and facies associations. Emphasis is placed on linking practical work and lectures. Exercises will be conducted in the field and in the laboratory. Students will be taught to log sedimentary sections and to map sediments and sedimentary rocks, to take samples and perform basic sedimentological analyses of physical properties in the lab.

A 7-week intensive course (first 7 weeks of fall term). 

Taught if sufficient number of students. May be taught as a reading course.

Occurrence of groundwater, the water content of soil, properties and types of aquifers (porosity, retention, yield, storage coefficients; unconfined, confined, leaky, homogeneous, isotropic aquifers). Principles of groundwater flow. Darcy's law, groundwater potential, potentiometric surface, hydraulic conductivity, transmissivity, permeability, determination of hydraulic conductivity in homogeneous and anisotropic aquifers, permeability, flow lines and flow nets, refraction of flow lines, steady and unsteady flow in confined, unconfined and leaky aquifers, general flow equations. Groundwater flow to wells, drawdown and recovery caused by pumping wells, determination of aquifer parameters from time-drawdown data, well loss, capacity and efficiency. Sea-water intrusion in coastal aquifers. Mass transport of solutes by groundwater flow. Quality and pollution of groundwater. Case histories from groundwater studies in Iceland. Numerical models of groundwater flow.   Students carry out an interdisciplinary project on groundwater hydrology and management.

Volcanic eruptions are one of the principal forces that affect and modify the Earth’s surface. The resulting volatile emissions not only replenish and maintain our atmosphere, but are also known to have significant impact atmospheric properties and its circulation. Volcanism has also played a critical role in forming a significant fraction of mineral resources currently exploited by man. As such, volcanic phenomena influence directly or indirectly many (if not all) sub-disciplines of Earth Sciences. Consequently, a basic understanding of how volcanoes work and how they contribute to the earth system cycles is a valuable knowledge to any student in geosciences.

The basic principles of volcanology are covered in this course including the journey of magma from source to surface plus the general processes that control eruptions and dispersal of erupted products. We also cover the principles of eruption monitoring as well as volcano-climate.

Practical sessions will be held weekly and are aimed at solving problems via calculations, data analysis and arguments. One field trip to Reykjanes.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Properties of liquids and gases. Pressure and force fields in liquids at rest, pressure gauges. Equations of motion, continuity, momentum and energy. Bernoulli equation of motion. Dimensional analysis and dynamic similarity. Two dimensional flow, non-viscous fluids, boundary layers theory, laminar and turbulent flow, fluid friction and form drag. Flow of compressible fluids, velocity of sound. Mach number, sound waves, nozzle shape for supersonic speed. Open channel flow. Several experiments are conducted.

Stress and strain tensors, wave-equations for P- and S-waves. Body waves and guided waves. Seismic waves: P-, S-, Rayleigh- and Love-waves. Free oscillations of the Earth. Seismographs, principles and properties. Sources of earthquakes: Focal mechanisms, seismic moment, magnitude scales, energy, frequency spectrum, intensity. Distribution of earthquakes and depths, geological framework. Seismic waves and the internal structure of the Earth.

The course is either tought in a traditional way (lectures, exercises, projects) or as a reading course where the students read textbooks and give a written or oral account of their studies.

The field excursion abroad has the aim to create first-hand experience with respect to the recognition of rock types which do not occur in Iceland and which typically have relatetively high stratigraphic ages (mostly Devonian to Eocene, ca. 400-40 Ma). The excursion will lead us to the "classical square miles in geology" at the northern margin of the Harz Mountains in central Germany. It will encompass the Harz Mountains and its northern foreland, a region listed as one of six UNESCO Global Geoparks in Germany since 2005 (Geopark Harz - Braunschweiger Land - Ostfalen). We will visit natural exposures, old and working quarries, and mines including the visitor mine of Rammelsberg in Goslar which became UNESCO World Heritage Site in 1992.

Igneous and metamorphic rocks such as granites and gneisses, and sedimentary rocks such as sandstones, shales and limestones including reef carbonates will be examined in the field. Karst features and speleothem formation will be explored. Massive Permian rock-salt deposits will be investigated in a mine 670 m below the surface. Eocene lignite deposits will be visited.

This course is only intended for Icelandic undergraduate students.

Students cover all expenses for travel and accommodation including entrance tickets for mines, caves and museum exhibitions apart from the rental of a bus.

The field trip will be from May 18 to 27.

Required equipment:

Slopes can be covered by scree material, and hikes of 5-15 km can be included. Thus, robust shoes are required. In addition, students should bring:

• a field book and pen(s),
• a geological compass,
• a hand lens,
• a scale for photos,
• safety goggles,
• and possibly work gloves.

Temperatures in May can be relatively warm and sun protection (cream, hat, long sleeve shirt) might be useful.

Glaciers are closely connected to the climate system as they both result from it and have impact on it. Glaciers are also important agents of erosion and deposition and the shaping of glacierized landscapes. This course studies glaciers and glacial landscapes with focus on their interaction with both the atmosphere and their substrate. Distribution and classification of glaciers in the world, the formation of glacier ice, glacier mass balance, hydrology, and movement will be discussed, as well as the processes and products of glacial erosion, deposition, and deformation and how they can be used for interpreting past and present glacier state and dynamics. The focus will be on Icelandic glaciers and their foreland geomorphology as signature of past behaviour.

During the course, students will learn terminology and concepts that will equip them to understand and contribute to discussions on the role of glaciers in the climate system in the context of past glacier extent as analysed from the sediment-landform record. Background in high school physics and math is useful, as well as sedimentology and physical geography. At the end of the course, 4-5 day field trip will be run to glaciers on the south coast of Iceland where glacier measurement techniques will be introduced with ablation stakes installed in Sólheimajökull, and students will get hands-on experience in documenting glacial sediments and geomorphology in selected glacier forelands.

Hydrology is the scientific study of earth's water resources. Students will be introduced to the physical and chemical properties of water and the processes responsible for its occurrence, distribution and cycling, with emphasis on the terrestrial phase of the hydrologic cycle as well as the characteristics of the Icelandic water resource. Methods and models used in engineering hydrology and design are introduced, and used to solve projects.

Glaciers in the world are responding fast to climate change, they are therefore important indicators for assessing changes, but have also impact on the climate system through for example albedo feedback and sea level rise. In this course glaciers will be studied, their distribution in the world, how glacier ice is formed from snow, how they move and respond to climate change.  Focus will be on Icelandic glaciers, their energy and mass balance, interaction of geothermal activity and glaciers in Iceland and reoccurring floods, jökulhlaups, from the main ice cap. During the course students will learn terminology and concepts that will equip them to understand and contribute to discussions of climate change and the role of glaciers in the climate system.  Background in high school physics and math is useful, as numerical  problems concerning temperature, energy budget, mass balance and flow of glaciers will be solved in groups. Glacier measurement techniques will be introduced and at the end of the course ablation stakes will be installed in Sólheimajökull on the south coast of Iceland in a two day fielld excursion. Participation in the field trip is mandatory.

The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the geological history of Iceland. Regional stratigraphies. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

Practical work: Weakly written exercises, seminars and reports. Students give talks on selected topics and write reports.

Excursions: Two-day excursion to Snæfellsnes peninsula OR two day-trips to West Iceland and Reykjanes Peninsula.

The aim of the course is to improve the student´s understanding of Earth´s history as well as Earth´s surface processes within a range of geological environments through the Cenozoic.

The basic principles of chemical equilibrium in metamorphic petrology is introduced followed by overview of basic types of metamorphism and metamorphic rocks. Various aspects are covered, including temperature and pressure of metamorphism, time and metamorphism, metamorphic reactions, geothermal gradients, fluid-rock interaction in hydrothermal systems, fluid origin, isotopes, geochemical structure of hydrothermal systems. The course consists of lectures and practices with microscopic examination of metamorphic rocks, calculation of the R-T dependence of metamorphic reactions, short essays and discussion.

Introduction to crystallography and mineralogy. Lectures cover four main fields: 1) Crystallography; 2) Crystal optics; 3) Crystal chemistry; 4) Systematic mineralogy where the students get familiar with the chemical composition and physical properties of the most important rock-forming minerals.

Laboratory work will include exercises with crystal models and optical microscope as well as determination of minerals in hand specimen.

During the course, group projects will also be issued. These projects are optional and the groups present their results at the end of the semester.

Continuum mechanics: Stress and strain, equations of motion. Seismic waves. Maxwell's equations and electromagnetic waves. Plane waves, reflection and refraction. Distributions and Fourier transforms. Fundamental solutions of linear partial differential equation. Waves in homogeneous media. Huygens' principle and Ásgeirsson's mean value theorem. Dispersion, phase and group velocities, Kramers-Kronig equations. The method of stationary phase. Surface waves on liquids.

In this course the student will learn about the origin, generation and evolution of magmas on Earth. A special consideration will be given to processes related to evolution and modification of magma as it passes through the crust.

Lectures will cover physics, chemistry and phase relations of magmas in mantle and crustal environments and igneous thermobarometry.

Practical sessions will cover basic methods of assessing magma origin and evolution. These include phase equilibria/thermodynamics; thermobarometry calculations; and modeling partial melting and fractional crystallization processes. Special emphasis will be on data interpretation and understanding uncertainties during data processing.  
The course runs for 7 weeks in the first half of the spring semester (weeks 1-7) and includes 3 lectures and 4 practical sessions per week.

This course deals with processes of glacial erosion, glacial sedimentation and glacial morphology. It is aimed at undergraduate students interested in physical geography, glacial geology and glaciology. Lectures will concern glacial systems, glacier movements, hydrology, erosion, sediment transport and deposition, glaciotectonic deformations, glacial landforms. The course ends with a 5-day field trip to present glaciers in southern Iceland and formerly glaciated areas in western Iceland, where students get to observe glacial processes and products. Participation in fieldtrip is required for getting course credits.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

Basic concepts in probability and statistics based on univariate calculus. 

Topics: 
Sample space, events, probability, equal probability, independent events, conditional probability, Bayes rule, random variables, distribution, density, joint distribution, independent random variables, condistional distribution, mean, variance, covariance, correlation, law of large numbers, Bernoulli, binomial, Poisson, uniform, exponential and normal random variables. Central limit theorem. Poisson process. Random sample, statistics, the distribution of the sample mean and the sample variance. Point estimate, maximum likelihood estimator, mean square error, bias. Interval estimates and hypotheses testing form normal, binomial and exponential samples. Simple linear regression. Goodness of fit tests, test of independence.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

 This course is an advanced graduate course in tectonics and structural geology, held in English, related to plate boundaries that takes place during 8 weeks in the Spring Semester every other year. This course is a combination of lectures, seminars (i.e. group discussions), and fieldwork using a world-class tectonic and structural laboratory – Iceland! Fieldwork will be a combination of group projects, reporting, and presentations of the results. Tectonics and structural geology controls many important elements of geosystems including: a) global climate (i.e. when the planet is relatively warm or cold), b) geological hazards, where and when and how earthquakes and volcanic eruptions take place, c) location and distribution of natural resources, etc. d) geological engineering problems. This course will explore advanced topics related to these and explore methods including modern field techniques, digital mapping, drone mapping, geophysical prospecting in order to explore structural and tectonic problems. Literature including state of the art peer-reviewed papers will be part of the readings as well as textbook and “classic papers”. Guest lectures, (depending on year), will be given by experts in their field (typically 2 lectures per year) and will involve topics such as: earthquake nucleation and physics-based fault and earthquake modelling, structures and ore bodies, paleomagnetism, paleoseismology, tectonophysical controls on volcanism, igneous intrusions (i.e. dikes and laccoliths). Specific topics that will be addressed yearly are: structural controls on geothermal systems including fluids in faults, structural and tectonic controls of volcanism, tectonic controls of geological hazards, tectonic geomorphology including ideas related to rock and surface uplift, paleoseismology, and neotectonics. Advanced undergraduates are welcome to contact the supervisory Professor if they can demonstrate suitable experience for participating in this exciting course that uses the Plate Boundary of Iceland as part of the learning experience.

The aim of the course is threefold:

• to identify which geological observations and methods are used to decipher Iceland's geological history,
• to analyze the limitations of methods and data
• to identify and explain with examples the main events in Iceland's geological history and the associated geological processes at work. 

Topics covered include the opening of the North Atlantic, the formation of tectonic plate boundaries (the Reykjanes, Kolbeinsey and Ægir ridges). The interaction of the Iceland hotspot with the tectonic plates, rift jumps and the formation of the igneous rock provinces of the North Atlantic will be discussed in the context of the formation of Iceland's bedrock. In addition, the course will address Iceland's past climate, environmental and glacial history, as well as geomorphological evolution. Discussion on the geological history of Iceland is placed in the context with the global conditions that existed when Iceland was being formed and shaped.

Teaching arrangement: This is a 7.5 ECTS course running over 14 weeks. Course material is delivered through lectures, selected readings, and three field trips. Lectures take place once per week (2 × 80 minutes). Attendance on field trips is mandatory.

Teaching statement: To achieve good results in the course, students need to actively participate in lectures and project work. Students gain knowledge in lectures, but it is necessary to do exercises and participate in field trips to increase understanding of concepts and train methods. Teachers will make course concepts and content accessible, but students are expected to study independently and ask questions if something is unclear. Teachers emphasize that students participate in the course evaluation if something needs to be improved. A midterm survey will be reviewed with the students.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Main emphasis is on the differential and integral calculus of functions of a single variable. The systems of real and complex numbers. Least upper bound and greatest lower bound. Natural numbers and induction. Mappings and functions. Sequences and limits. Series and convergence tests. Conditionally convergent series. Limits and continuous functions. Trigonometric functions. Differentiation. Extreme values. The mean value theorem and polynomial approximation. Integration. The fundamental theorem of calculus. Logarithmic and exponential functions, hyperbolic and inverse trigonometric functions. Methods for finding antiderivatives. Real power series. First-order differential equations. Complex valued functions and second-order differential equations.

Introduce students to methods and fundamental laws of mechanics, waves and thermodynamics, to the extent that they can apply their knowledge to solve problems. 

Concepts, units, scales and dimensions.  Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body.  Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound.  Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics.

Note that the textbook is accessible to students via Canvas free of charge.

There are 4 lab sessions with experiments mainly from mechanics, with emphasis on teaching students methods of data collection and data processing. Student hand in a lab report on each experiment. They also hand in a final report from one of these that is intended to look more like a journal article.

The course emphasizes geological processes as a consequence of endogenic processes.

Main topics covered in the course:

• The main features of the Earth’s internal structure, with emphasis on its layering and the properties of individual layers.
• Early hypotheses about continental drift and their development leading to plate tectonics theory, with emphasis on why and how the relative positions of plates and continents are constantly changing.
• The fundamentals of mineral and rock formation and metamorphism.
• Volcanism: causes, distribution, and hazards, with special reference to Iceland.
• Causes of earthquakes and their distribution, different types and behavior of seismic waves, and how this knowledge can be used, for example, to locate and assess the size of earthquakes.
• Structural geology: faults, folds, mountain building, and associated forces.
• Geological time and dating methods, and the geologic time scale, i.e., the arrangement of strata in time and space.
• In addition to general discussion of the course content, special emphasis is placed on the geological and geohistorical formation and position of Iceland.

Teaching Arrangement

The course is 7.5 ECTS and spans 14 weeks. Course content is presented in lectures, selected reading material, practical exercises, and three field trips.

• Lectures are tvice a week inaddtion to on excercise class.
• Field trips: Day trips, usually during the first 4–5 weeks of the semester. Attendance is mandatory. Note field trips can be on weekends.
• Practical exercises: Conducted in classrooms and around the University. Attendance is mandatory.
• Chapter quizzes: Weekly multiple-choice quizzes on textbook chapters. Each quiz is 10 minutes, taken at the beginning of Monday lectures, linked to individual chapters.

Assessment

Assessment is threefold, and all components must be passed with a minimum grade of 5 to pass the course.

• In class exams: 20%
• Field trips and practical exercises: 30%
• Written final exam: 50%

Required Texts and Materials

• Earth – Portrait of a Planet (required). Second half of the book is used in JAR202G.
• Geological Field Techniques (required – pdf provided).
• Compass with clinometer (required).
• Good field notebook (required).
• Hammer, hand lens (recommended).

Teaching Statement

To succeed in this course, students must actively participate in lectures and assignments. Knowledge is gained through lectures and readings, but assignments and field trips are essential to deepen understanding and practice methods. Teachers will make key concepts and materials accessible, but students are expected to learn independently and ask questions if unclear. Teachers emphasize participation in course evaluations to address improvements. The midterm survey will be reviewed with students after completion.

Code of Conduct

Great emphasis is placed on honest academic work in accordance with the University of Iceland’s Code of Ethics:
https://www.hi.is/haskolinn/sidareglur
If a student is found guilty of misconduct in exams or coursework, action will be taken as outlined in the University’s regulations:
https://ugla.hi.is/kennsluskra/index.php?tab=skoli&chapter=content&id=46779

Turnitin

Assignments in this course will be checked using Turnitin.

Artificial Intelligence

Use of AI in studies at the University of Iceland is governed by university guidelines:
https://gervigreind.hi.is/
In this course, the use of AI in assignments and/or exams is not permitted unless explicitly allowed by the instructors. Any uncertainty regarding AI use must be clarified with the course coordinator.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Tutor classes for Earth Science students

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Emphasis is laid on the theoretical aspects of the material. The aim is that the students acquire understanding of fundamental concepts and are able to use them, both in theoretical consideration and in calculations. Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobian matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flows. Cylindrical and spherical coordinates. Taylor polynomials. Extrema and classification of stationary points. Extrema with constraints. Implicit functions and local inverses. Line integrals and potential functions. Proper and improper multiple integrals. Change of variables in multiple integrals. Simply connected regions. Integration on surfaces. Theorems of Green, Stokes and Gauss.

Introduction to electrodynamics in material; from insulators to superconductors.  Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics.

There are four 4 hour lab sessions and two 3 hour sessions, from optics and electromagnetism. Students hand in a lab report on each experiment. They also hand in a final report from one of the 4 hour experiments that is intended to look more like a journal article.

This course focuses on the Earth Surface processes, specifically those that contribute to the formation of various landforms and landscapes and how these landforms evolve and erode over time and space. Emphasis is placed on enabling students to discuss these geological processes using geological terminology in both Icelandic and English.

Key topics include:

• Basic sedimentology, with a focus on changes in grain size, distribution, and texture of rock particles during transport by running water, glaciers, and wind.
• Earth's water cycle and its significant role in shaping terrestrial landscapes through weathering, erosion, and deposition of rock material.
• Running water as the most influential agent in shaping Earth's land surfaces through both erosion and transport of rock debris.
• Coastal dynamics and factors influencing shoreline development, highlighting the ongoing changes, fast and slow, at the land-sea boundary.
• Groundwater's role in land formation, its importance for drinking water supply, and measures to protect this vital resource.
• The Earth's atmospheric circulation, its influence on precipitation patterns, and the distribution of arid and vegetative areas.
• Erosional and depositional processes and their role in landform development in Iceland, focusing on glaciation and its history, especially during the last ice age.
• Discussion of Earth's inorganic and organic resources, their formation, distribution, extraction, usage, disposal, renewal, and recycling.
• Special emphasis is placed on relating the theoretical aspects of the course to Iceland by exploring relevant local examples.

Teaching Arrangement

The course is worth 7.5 ECTS and spans 14 weeks. Material is presented through lectures, selected readings, and a 5-day field trip to South Iceland and the Westman Islands. The primary purpose of the field trip is to provide students with direct experience of the processes and landforms covered in the course. The field trip takes place immediately after the spring exams and is mandatory. Students must cover their own meal expenses during the trip. Weekly multiple-choice exams related to textbook chapters are assigned.

Teaching Statement

For students to succeed in this course, active participation in lectures and assignments is key. Students will gain knowledge through lectures and reading material but completing assignments and attending field trips are essential for deepening understanding of key concepts and methods. Instructors will make course concepts accessible, but students are expected to learn independently and ask questions if anything is unclear. Instructors emphasize the importance of student feedback through course evaluations to address areas for improvement, with a mid-term evaluation reviewed with students.

Assessment

The course assessment is three-fold, and all parts must be completed with a minimum grade of 5 to pass the course.

• Multiple choice exams: 25%

• Field trip journal: 15%
• Written final exam: 60%

Learning Outcomes:

Upon completing the course, students should be able to:

• Use geological terminology to discuss the natural environment of the land.
• Explain the role of Earth's exogenic forces in the ever-changing appearance of its land surface.
• Provide examples of how the effects of these exogenic forces vary across time and space.
• Analyze the role of exogenic forces in shaping individual landforms and landscapes.
• Identify individual landforms and landscapes and link them to one or more exogenic processes.
• Analyze composite evidence of exogenic processes and use that analysis to describe the sequence of events, in time and space, that created specific landforms and landscapes.
• Read geological maps that show surface deposits.
• Record and manage their own observations in a field notebook.

An introduction to the physics of the Earth. Origin and age of the Earth. Dating with radioactive elements. Gravity, shape and rotation of the Earth, the geomagnetic field, magnetic anomalies, palaeomagnetism, electric conductivity. Earthquakes, seismograph and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Geophysical research in Iceland.

Practicals include solving problems set for each week and exercises in the use of geophysical instruments.  Students write one essay on a selected topic in geophysics.

Basic principles and mathematical methods in thermodynamics,laws of thermodynamics, state functions, Maxwell relations, equilibrium, phase transitions, quantum statistical mechanics, ideal and real gases, specific heat, rate theory, Bose and Fermi distributions.

The objective of the course is to teach the student the basic concepts of thermodynamic systems. The students should also understand different forms of energy, energy transport and conversion from one state to another. The student should be able to calculate the rates of chemical reactions and energy balance.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

Programming in Python (for computations in engineering and science): Main commands and statements (computations, control statements, in- and output), definition and execution of functions, datatypes (numbers, matrices, strings, logical values, records), operations and built-in functions, array and matrix computation, file processing, statistics, graphics. Object-oriented programming: classes, objects, constructors and methods. Concepts associated with design and construction of program systems: Programming environment and practices, design and documentation of function and subroutine libraries, debugging and testing of programmes.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

The course is aimed at students that have already taken a first course in geophysics and have basic knowledge of geophysical exploration and its application.  The course is split in two parts:

1. a) Four to five days of field work at the beginning of autumn term.  Several geophysical methods applied to practical problems.
2. b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computation excises and model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Goal: To teach students the properties of electronic components and circuits, measurement technologies and train them in methods and solutions for electronic circuit design, measurements, research and data acquisition. 

Curriculum: The course covers fundamental issues in electronics, the physics of electronics and electronic components and measurement technology. The curriculum includes theory and practical analysis of AC and dc circuits, diodes and transistors, operational amplifiers and feedback, logic components and digital circuits, digital measurement techniques, amplification and filtering. The course includes twelve laboratory sessions and a project on a microcomputer controlled measurement system. The course concludes with a written exam.

The equations of Laplace and Poisson. Magnetostatics. Induction.  Maxwell's equations. Energy of the electromagnetic field. Poynting's theorem. Electromagnetic waves. Plane waves in dielectric and conducting media, reflection and refraction.  Electromagnetic radiation and scattering. Damping.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

Basic concepts of thermodynamic systems, the zeroth law of thermodynamics. Work, internal energy, heat, enthalpy, the first law of thermodynamics for closed and open systems. Ideal and real gases, equations of state. The second law of thermodynamics, entropy, available energy. Thermodynamic cycles and heat engines, cooling engines and heat pumps. Thermodynamic potentials, Maxwell relations. Mixture of ideal gases. Properties for water and steam. Chemical potentials, chemical reactions of ideal gases, the third law of thermodynamics.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Geological and environmental history of the Earth from the Precambrian, Palaeozoic, Mesozoic, and Cenozoic to present. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, Wilson Cycle, climate history and evolution of life. Fossils, basic principles of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Icehouse and greenhouse Earth and climate change in general. The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the location that will eventually become Iceland. Gradual climate cooling during Cenozoic and implications. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Objectives:   To introduce continuum mechanics, fluid dynamics and heat transfer and their application to problems in physics and geophysics. I. Stress and strain, stress fields, stress tensor, bending of plates, models of material behaviour: elastic, viscous, plastic materials. II. Fluids, viscous fluids, laminar and turbulent flow, equation of continuity, Navier-Stokes equation. III. Heat transfer: Heat conduction, convection, advection and geothermal resources. Examples and problems from various branches of physics will be studied, particularly from geophysics.

Teaching statement: To do well in this course, students should actively participate in the discussions, attend lectures, give student presentations and deliver the problem sets assigned in the course. Students will gain knowledge through the lectures, but it is necessary to do the exercises to understand and train the use of the concepts. The exercises are intergrated in the text of the book, it is recommended to do them while reading the text. Instructors will strive to make the concepts and terminology accessible, but it is expected that students study independently and ask questions if something is unclear. In order to improve the course and its content, it is appreciated that students participate in the course evaluation, both the mid-term and the end of term course evaluation.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

The aim is to introduce students to the disciplines of general oceanography, in particular marine geological, physical and chemical oceanography. To understand how the interactions of processes shape the characteristics of different ocean regions.
The course covers the distribution of land and water, the world oceans and their geomorphology. Instruments and techniques in oceanographic observations. Physical properties of sea water. Energy and water budgets. Distribution of properties in relation to turbulence and diffusion. Introductory dynamical oceanography. Chemical oceanography: Geochemical balance, major and minor elements, dissolved gases. Biogeochemical cycles. Biological processes in relation to the physical and chemical environment. Oceanography of the North Atlantic and Icelandic waters

Students work on the BS-project under the supervision of a teacher.

Geological history of the Precambrian, Palaeozoic and Mesozoic. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, climate history and evolution of life. Fossils and stratigraphy, basic priciples of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Practical work: Written exercises, seminars and reports. Students give seminars and write reports on selected subjects.

Tectonic motions control the nature of the planet we inhabit and the location of continents, mountain ranges, volcanoes, where earthquakes occur and even are important for controlling the Earth's climate. Structural geology and crustal movements in the world, with special emphasis on movements in Iceland. This course introduces the techniques of structural geology through a survey of the mechanics of rock deformation, a survey of the features and geometries of faults and folds, and techniques of strain analysis. Regional structural geology and tectonics are introduced. The subject of the course is active tectonic movements and how this is manifested and recorded in the geological record with emphasis on processes currently active in Iceland. Lectures will be complimented with fieldwork and supportive examples will be given from a global perspective (e.g. compressional tectonics from the Andes and other extensional environments like the East Africa Rift). Methods to describe these processes will be taught and evaluated. Structural geology concepts including elastic, ductile, and brittle behavior of rocks in the crust and mantle will be discussed and discontinuities and brittle fracturing will be addressed. Plate tectonics, plate velocity models, both relative and absolute. Earthquakes. Plate boundary deformation including strike-slip, extensional, and compressive regimes with rifts and rifting structures and folds in addition to mountain building. (If time permits: microstructures, post-rifting and post-seismic movements, Isostasy, vertical crustal movements and sea level, and structural level. measuring crustal movements, GPS-geodesy, levelling, and analysis of seismic stratigraphy (i.e. active source seismic reflection and refraction profiles). Fieldwork will focus on discontinuity analysis and characterisation through a combination of exposure mapping with structural observations coupled with digital elevation (DEMs) model collection using drones and associated analysis to create a coherent assessment of active faults in Southwestern Iceland. Lectures are required as content in the lectures will be tested. Students visiting from abroad in Geology and Geophysics are encouraged to participate in this class as this will be held in English and provide excellent insight into the Iceland Tectonic and Plate Boundary system. 

The aim of the course is to give a comprehensive summary of the environmental change that occurred during the Quaternary period with special reference to Iceland. Contents: The characteristics of the Quaternary and geological evidence for global climatic change. Variations of Earth´s orbital parameters. Dating methods. Glacial debris transport and glacial sedimentation on land and in water. Evidence for climate change in glacier ice and marine and lake sediment. Volcanic activity and the environment. Paleoclimate reconstruction. The glacial and climatic history of Iceland and the North Atlantic Ocean. Grading: Final project 35%, assignments during the semester 30%, presentations 15%, Take home exam 20%. Part of the term project will be a comprehensive search for references to be used by students as they write their term paper and prepare a presentation to be given in class.

Heat budget of the Earth, heat transport to the Earth´s surface. Geothermal systems and their structure, renewability of geothermal systems, methodology in geothermal development, estimation of resource size, fluid origin and chemistry, water-rock interaction, environmental impact of utilization, well testing and well data integration.  The course is taught during 7-week period in the first part of the fall semester.  It consists of lectures, practical, student lectures, student posters, essay and exams.  The course is taught in English.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

The course will focus on the study of sediments and sedimentary rocks, erosion, transport processes and accumulation of sediments, and sedimentary facies and facies associations. Emphasis is placed on linking practical work and lectures. Exercises will be conducted in the field and in the laboratory. Students will be taught to log sedimentary sections and to map sediments and sedimentary rocks, to take samples and perform basic sedimentological analyses of physical properties in the lab.

A 7-week intensive course (first 7 weeks of fall term). 

Taught if sufficient number of students. May be taught as a reading course.

Occurrence of groundwater, the water content of soil, properties and types of aquifers (porosity, retention, yield, storage coefficients; unconfined, confined, leaky, homogeneous, isotropic aquifers). Principles of groundwater flow. Darcy's law, groundwater potential, potentiometric surface, hydraulic conductivity, transmissivity, permeability, determination of hydraulic conductivity in homogeneous and anisotropic aquifers, permeability, flow lines and flow nets, refraction of flow lines, steady and unsteady flow in confined, unconfined and leaky aquifers, general flow equations. Groundwater flow to wells, drawdown and recovery caused by pumping wells, determination of aquifer parameters from time-drawdown data, well loss, capacity and efficiency. Sea-water intrusion in coastal aquifers. Mass transport of solutes by groundwater flow. Quality and pollution of groundwater. Case histories from groundwater studies in Iceland. Numerical models of groundwater flow.   Students carry out an interdisciplinary project on groundwater hydrology and management.

Volcanic eruptions are one of the principal forces that affect and modify the Earth’s surface. The resulting volatile emissions not only replenish and maintain our atmosphere, but are also known to have significant impact atmospheric properties and its circulation. Volcanism has also played a critical role in forming a significant fraction of mineral resources currently exploited by man. As such, volcanic phenomena influence directly or indirectly many (if not all) sub-disciplines of Earth Sciences. Consequently, a basic understanding of how volcanoes work and how they contribute to the earth system cycles is a valuable knowledge to any student in geosciences.

The basic principles of volcanology are covered in this course including the journey of magma from source to surface plus the general processes that control eruptions and dispersal of erupted products. We also cover the principles of eruption monitoring as well as volcano-climate.

Practical sessions will be held weekly and are aimed at solving problems via calculations, data analysis and arguments. One field trip to Reykjanes.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Properties of liquids and gases. Pressure and force fields in liquids at rest, pressure gauges. Equations of motion, continuity, momentum and energy. Bernoulli equation of motion. Dimensional analysis and dynamic similarity. Two dimensional flow, non-viscous fluids, boundary layers theory, laminar and turbulent flow, fluid friction and form drag. Flow of compressible fluids, velocity of sound. Mach number, sound waves, nozzle shape for supersonic speed. Open channel flow. Several experiments are conducted.

Stress and strain tensors, wave-equations for P- and S-waves. Body waves and guided waves. Seismic waves: P-, S-, Rayleigh- and Love-waves. Free oscillations of the Earth. Seismographs, principles and properties. Sources of earthquakes: Focal mechanisms, seismic moment, magnitude scales, energy, frequency spectrum, intensity. Distribution of earthquakes and depths, geological framework. Seismic waves and the internal structure of the Earth.

The course is either tought in a traditional way (lectures, exercises, projects) or as a reading course where the students read textbooks and give a written or oral account of their studies.

The field excursion abroad has the aim to create first-hand experience with respect to the recognition of rock types which do not occur in Iceland and which typically have relatetively high stratigraphic ages (mostly Devonian to Eocene, ca. 400-40 Ma). The excursion will lead us to the "classical square miles in geology" at the northern margin of the Harz Mountains in central Germany. It will encompass the Harz Mountains and its northern foreland, a region listed as one of six UNESCO Global Geoparks in Germany since 2005 (Geopark Harz - Braunschweiger Land - Ostfalen). We will visit natural exposures, old and working quarries, and mines including the visitor mine of Rammelsberg in Goslar which became UNESCO World Heritage Site in 1992.

Igneous and metamorphic rocks such as granites and gneisses, and sedimentary rocks such as sandstones, shales and limestones including reef carbonates will be examined in the field. Karst features and speleothem formation will be explored. Massive Permian rock-salt deposits will be investigated in a mine 670 m below the surface. Eocene lignite deposits will be visited.

This course is only intended for Icelandic undergraduate students.

Students cover all expenses for travel and accommodation including entrance tickets for mines, caves and museum exhibitions apart from the rental of a bus.

The field trip will be from May 18 to 27.

Required equipment:

Slopes can be covered by scree material, and hikes of 5-15 km can be included. Thus, robust shoes are required. In addition, students should bring:

• a field book and pen(s),
• a geological compass,
• a hand lens,
• a scale for photos,
• safety goggles,
• and possibly work gloves.

Temperatures in May can be relatively warm and sun protection (cream, hat, long sleeve shirt) might be useful.

Glaciers are closely connected to the climate system as they both result from it and have impact on it. Glaciers are also important agents of erosion and deposition and the shaping of glacierized landscapes. This course studies glaciers and glacial landscapes with focus on their interaction with both the atmosphere and their substrate. Distribution and classification of glaciers in the world, the formation of glacier ice, glacier mass balance, hydrology, and movement will be discussed, as well as the processes and products of glacial erosion, deposition, and deformation and how they can be used for interpreting past and present glacier state and dynamics. The focus will be on Icelandic glaciers and their foreland geomorphology as signature of past behaviour.

During the course, students will learn terminology and concepts that will equip them to understand and contribute to discussions on the role of glaciers in the climate system in the context of past glacier extent as analysed from the sediment-landform record. Background in high school physics and math is useful, as well as sedimentology and physical geography. At the end of the course, 4-5 day field trip will be run to glaciers on the south coast of Iceland where glacier measurement techniques will be introduced with ablation stakes installed in Sólheimajökull, and students will get hands-on experience in documenting glacial sediments and geomorphology in selected glacier forelands.

Hydrology is the scientific study of earth's water resources. Students will be introduced to the physical and chemical properties of water and the processes responsible for its occurrence, distribution and cycling, with emphasis on the terrestrial phase of the hydrologic cycle as well as the characteristics of the Icelandic water resource. Methods and models used in engineering hydrology and design are introduced, and used to solve projects.

Glaciers in the world are responding fast to climate change, they are therefore important indicators for assessing changes, but have also impact on the climate system through for example albedo feedback and sea level rise. In this course glaciers will be studied, their distribution in the world, how glacier ice is formed from snow, how they move and respond to climate change.  Focus will be on Icelandic glaciers, their energy and mass balance, interaction of geothermal activity and glaciers in Iceland and reoccurring floods, jökulhlaups, from the main ice cap. During the course students will learn terminology and concepts that will equip them to understand and contribute to discussions of climate change and the role of glaciers in the climate system.  Background in high school physics and math is useful, as numerical  problems concerning temperature, energy budget, mass balance and flow of glaciers will be solved in groups. Glacier measurement techniques will be introduced and at the end of the course ablation stakes will be installed in Sólheimajökull on the south coast of Iceland in a two day fielld excursion. Participation in the field trip is mandatory.

The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the geological history of Iceland. Regional stratigraphies. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

Practical work: Weakly written exercises, seminars and reports. Students give talks on selected topics and write reports.

Excursions: Two-day excursion to Snæfellsnes peninsula OR two day-trips to West Iceland and Reykjanes Peninsula.

The aim of the course is to improve the student´s understanding of Earth´s history as well as Earth´s surface processes within a range of geological environments through the Cenozoic.

The basic principles of chemical equilibrium in metamorphic petrology is introduced followed by overview of basic types of metamorphism and metamorphic rocks. Various aspects are covered, including temperature and pressure of metamorphism, time and metamorphism, metamorphic reactions, geothermal gradients, fluid-rock interaction in hydrothermal systems, fluid origin, isotopes, geochemical structure of hydrothermal systems. The course consists of lectures and practices with microscopic examination of metamorphic rocks, calculation of the R-T dependence of metamorphic reactions, short essays and discussion.

Introduction to crystallography and mineralogy. Lectures cover four main fields: 1) Crystallography; 2) Crystal optics; 3) Crystal chemistry; 4) Systematic mineralogy where the students get familiar with the chemical composition and physical properties of the most important rock-forming minerals.

Laboratory work will include exercises with crystal models and optical microscope as well as determination of minerals in hand specimen.

During the course, group projects will also be issued. These projects are optional and the groups present their results at the end of the semester.

Continuum mechanics: Stress and strain, equations of motion. Seismic waves. Maxwell's equations and electromagnetic waves. Plane waves, reflection and refraction. Distributions and Fourier transforms. Fundamental solutions of linear partial differential equation. Waves in homogeneous media. Huygens' principle and Ásgeirsson's mean value theorem. Dispersion, phase and group velocities, Kramers-Kronig equations. The method of stationary phase. Surface waves on liquids.

In this course the student will learn about the origin, generation and evolution of magmas on Earth. A special consideration will be given to processes related to evolution and modification of magma as it passes through the crust.

Lectures will cover physics, chemistry and phase relations of magmas in mantle and crustal environments and igneous thermobarometry.

Practical sessions will cover basic methods of assessing magma origin and evolution. These include phase equilibria/thermodynamics; thermobarometry calculations; and modeling partial melting and fractional crystallization processes. Special emphasis will be on data interpretation and understanding uncertainties during data processing.  
The course runs for 7 weeks in the first half of the spring semester (weeks 1-7) and includes 3 lectures and 4 practical sessions per week.

This course deals with processes of glacial erosion, glacial sedimentation and glacial morphology. It is aimed at undergraduate students interested in physical geography, glacial geology and glaciology. Lectures will concern glacial systems, glacier movements, hydrology, erosion, sediment transport and deposition, glaciotectonic deformations, glacial landforms. The course ends with a 5-day field trip to present glaciers in southern Iceland and formerly glaciated areas in western Iceland, where students get to observe glacial processes and products. Participation in fieldtrip is required for getting course credits.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

Basic concepts in probability and statistics based on univariate calculus. 

Topics: 
Sample space, events, probability, equal probability, independent events, conditional probability, Bayes rule, random variables, distribution, density, joint distribution, independent random variables, condistional distribution, mean, variance, covariance, correlation, law of large numbers, Bernoulli, binomial, Poisson, uniform, exponential and normal random variables. Central limit theorem. Poisson process. Random sample, statistics, the distribution of the sample mean and the sample variance. Point estimate, maximum likelihood estimator, mean square error, bias. Interval estimates and hypotheses testing form normal, binomial and exponential samples. Simple linear regression. Goodness of fit tests, test of independence.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

 This course is an advanced graduate course in tectonics and structural geology, held in English, related to plate boundaries that takes place during 8 weeks in the Spring Semester every other year. This course is a combination of lectures, seminars (i.e. group discussions), and fieldwork using a world-class tectonic and structural laboratory – Iceland! Fieldwork will be a combination of group projects, reporting, and presentations of the results. Tectonics and structural geology controls many important elements of geosystems including: a) global climate (i.e. when the planet is relatively warm or cold), b) geological hazards, where and when and how earthquakes and volcanic eruptions take place, c) location and distribution of natural resources, etc. d) geological engineering problems. This course will explore advanced topics related to these and explore methods including modern field techniques, digital mapping, drone mapping, geophysical prospecting in order to explore structural and tectonic problems. Literature including state of the art peer-reviewed papers will be part of the readings as well as textbook and “classic papers”. Guest lectures, (depending on year), will be given by experts in their field (typically 2 lectures per year) and will involve topics such as: earthquake nucleation and physics-based fault and earthquake modelling, structures and ore bodies, paleomagnetism, paleoseismology, tectonophysical controls on volcanism, igneous intrusions (i.e. dikes and laccoliths). Specific topics that will be addressed yearly are: structural controls on geothermal systems including fluids in faults, structural and tectonic controls of volcanism, tectonic controls of geological hazards, tectonic geomorphology including ideas related to rock and surface uplift, paleoseismology, and neotectonics. Advanced undergraduates are welcome to contact the supervisory Professor if they can demonstrate suitable experience for participating in this exciting course that uses the Plate Boundary of Iceland as part of the learning experience.

The aim of the course is threefold:

• to identify which geological observations and methods are used to decipher Iceland's geological history,
• to analyze the limitations of methods and data
• to identify and explain with examples the main events in Iceland's geological history and the associated geological processes at work. 

Topics covered include the opening of the North Atlantic, the formation of tectonic plate boundaries (the Reykjanes, Kolbeinsey and Ægir ridges). The interaction of the Iceland hotspot with the tectonic plates, rift jumps and the formation of the igneous rock provinces of the North Atlantic will be discussed in the context of the formation of Iceland's bedrock. In addition, the course will address Iceland's past climate, environmental and glacial history, as well as geomorphological evolution. Discussion on the geological history of Iceland is placed in the context with the global conditions that existed when Iceland was being formed and shaped.

Teaching arrangement: This is a 7.5 ECTS course running over 14 weeks. Course material is delivered through lectures, selected readings, and three field trips. Lectures take place once per week (2 × 80 minutes). Attendance on field trips is mandatory.

Teaching statement: To achieve good results in the course, students need to actively participate in lectures and project work. Students gain knowledge in lectures, but it is necessary to do exercises and participate in field trips to increase understanding of concepts and train methods. Teachers will make course concepts and content accessible, but students are expected to study independently and ask questions if something is unclear. Teachers emphasize that students participate in the course evaluation if something needs to be improved. A midterm survey will be reviewed with the students.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Main emphasis is on the differential and integral calculus of functions of a single variable. The systems of real and complex numbers. Least upper bound and greatest lower bound. Natural numbers and induction. Mappings and functions. Sequences and limits. Series and convergence tests. Conditionally convergent series. Limits and continuous functions. Trigonometric functions. Differentiation. Extreme values. The mean value theorem and polynomial approximation. Integration. The fundamental theorem of calculus. Logarithmic and exponential functions, hyperbolic and inverse trigonometric functions. Methods for finding antiderivatives. Real power series. First-order differential equations. Complex valued functions and second-order differential equations.

Introduce students to methods and fundamental laws of mechanics, waves and thermodynamics, to the extent that they can apply their knowledge to solve problems. 

Concepts, units, scales and dimensions.  Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body.  Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound.  Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics.

Note that the textbook is accessible to students via Canvas free of charge.

There are 4 lab sessions with experiments mainly from mechanics, with emphasis on teaching students methods of data collection and data processing. Student hand in a lab report on each experiment. They also hand in a final report from one of these that is intended to look more like a journal article.

The course emphasizes geological processes as a consequence of endogenic processes.

Main topics covered in the course:

• The main features of the Earth’s internal structure, with emphasis on its layering and the properties of individual layers.
• Early hypotheses about continental drift and their development leading to plate tectonics theory, with emphasis on why and how the relative positions of plates and continents are constantly changing.
• The fundamentals of mineral and rock formation and metamorphism.
• Volcanism: causes, distribution, and hazards, with special reference to Iceland.
• Causes of earthquakes and their distribution, different types and behavior of seismic waves, and how this knowledge can be used, for example, to locate and assess the size of earthquakes.
• Structural geology: faults, folds, mountain building, and associated forces.
• Geological time and dating methods, and the geologic time scale, i.e., the arrangement of strata in time and space.
• In addition to general discussion of the course content, special emphasis is placed on the geological and geohistorical formation and position of Iceland.

Teaching Arrangement

The course is 7.5 ECTS and spans 14 weeks. Course content is presented in lectures, selected reading material, practical exercises, and three field trips.

• Lectures are tvice a week inaddtion to on excercise class.
• Field trips: Day trips, usually during the first 4–5 weeks of the semester. Attendance is mandatory. Note field trips can be on weekends.
• Practical exercises: Conducted in classrooms and around the University. Attendance is mandatory.
• Chapter quizzes: Weekly multiple-choice quizzes on textbook chapters. Each quiz is 10 minutes, taken at the beginning of Monday lectures, linked to individual chapters.

Assessment

Assessment is threefold, and all components must be passed with a minimum grade of 5 to pass the course.

• In class exams: 20%
• Field trips and practical exercises: 30%
• Written final exam: 50%

Required Texts and Materials

• Earth – Portrait of a Planet (required). Second half of the book is used in JAR202G.
• Geological Field Techniques (required – pdf provided).
• Compass with clinometer (required).
• Good field notebook (required).
• Hammer, hand lens (recommended).

Teaching Statement

To succeed in this course, students must actively participate in lectures and assignments. Knowledge is gained through lectures and readings, but assignments and field trips are essential to deepen understanding and practice methods. Teachers will make key concepts and materials accessible, but students are expected to learn independently and ask questions if unclear. Teachers emphasize participation in course evaluations to address improvements. The midterm survey will be reviewed with students after completion.

Code of Conduct

Great emphasis is placed on honest academic work in accordance with the University of Iceland’s Code of Ethics:
https://www.hi.is/haskolinn/sidareglur
If a student is found guilty of misconduct in exams or coursework, action will be taken as outlined in the University’s regulations:
https://ugla.hi.is/kennsluskra/index.php?tab=skoli&chapter=content&id=46779

Turnitin

Assignments in this course will be checked using Turnitin.

Artificial Intelligence

Use of AI in studies at the University of Iceland is governed by university guidelines:
https://gervigreind.hi.is/
In this course, the use of AI in assignments and/or exams is not permitted unless explicitly allowed by the instructors. Any uncertainty regarding AI use must be clarified with the course coordinator.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Tutor classes for Earth Science students

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Emphasis is laid on the theoretical aspects of the material. The aim is that the students acquire understanding of fundamental concepts and are able to use them, both in theoretical consideration and in calculations. Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobian matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flows. Cylindrical and spherical coordinates. Taylor polynomials. Extrema and classification of stationary points. Extrema with constraints. Implicit functions and local inverses. Line integrals and potential functions. Proper and improper multiple integrals. Change of variables in multiple integrals. Simply connected regions. Integration on surfaces. Theorems of Green, Stokes and Gauss.

Introduction to electrodynamics in material; from insulators to superconductors.  Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics.

There are four 4 hour lab sessions and two 3 hour sessions, from optics and electromagnetism. Students hand in a lab report on each experiment. They also hand in a final report from one of the 4 hour experiments that is intended to look more like a journal article.

This course focuses on the Earth Surface processes, specifically those that contribute to the formation of various landforms and landscapes and how these landforms evolve and erode over time and space. Emphasis is placed on enabling students to discuss these geological processes using geological terminology in both Icelandic and English.

Key topics include:

• Basic sedimentology, with a focus on changes in grain size, distribution, and texture of rock particles during transport by running water, glaciers, and wind.
• Earth's water cycle and its significant role in shaping terrestrial landscapes through weathering, erosion, and deposition of rock material.
• Running water as the most influential agent in shaping Earth's land surfaces through both erosion and transport of rock debris.
• Coastal dynamics and factors influencing shoreline development, highlighting the ongoing changes, fast and slow, at the land-sea boundary.
• Groundwater's role in land formation, its importance for drinking water supply, and measures to protect this vital resource.
• The Earth's atmospheric circulation, its influence on precipitation patterns, and the distribution of arid and vegetative areas.
• Erosional and depositional processes and their role in landform development in Iceland, focusing on glaciation and its history, especially during the last ice age.
• Discussion of Earth's inorganic and organic resources, their formation, distribution, extraction, usage, disposal, renewal, and recycling.
• Special emphasis is placed on relating the theoretical aspects of the course to Iceland by exploring relevant local examples.

Teaching Arrangement

The course is worth 7.5 ECTS and spans 14 weeks. Material is presented through lectures, selected readings, and a 5-day field trip to South Iceland and the Westman Islands. The primary purpose of the field trip is to provide students with direct experience of the processes and landforms covered in the course. The field trip takes place immediately after the spring exams and is mandatory. Students must cover their own meal expenses during the trip. Weekly multiple-choice exams related to textbook chapters are assigned.

Teaching Statement

For students to succeed in this course, active participation in lectures and assignments is key. Students will gain knowledge through lectures and reading material but completing assignments and attending field trips are essential for deepening understanding of key concepts and methods. Instructors will make course concepts accessible, but students are expected to learn independently and ask questions if anything is unclear. Instructors emphasize the importance of student feedback through course evaluations to address areas for improvement, with a mid-term evaluation reviewed with students.

Assessment

The course assessment is three-fold, and all parts must be completed with a minimum grade of 5 to pass the course.

• Multiple choice exams: 25%

• Field trip journal: 15%
• Written final exam: 60%

Learning Outcomes:

Upon completing the course, students should be able to:

• Use geological terminology to discuss the natural environment of the land.
• Explain the role of Earth's exogenic forces in the ever-changing appearance of its land surface.
• Provide examples of how the effects of these exogenic forces vary across time and space.
• Analyze the role of exogenic forces in shaping individual landforms and landscapes.
• Identify individual landforms and landscapes and link them to one or more exogenic processes.
• Analyze composite evidence of exogenic processes and use that analysis to describe the sequence of events, in time and space, that created specific landforms and landscapes.
• Read geological maps that show surface deposits.
• Record and manage their own observations in a field notebook.

An introduction to the physics of the Earth. Origin and age of the Earth. Dating with radioactive elements. Gravity, shape and rotation of the Earth, the geomagnetic field, magnetic anomalies, palaeomagnetism, electric conductivity. Earthquakes, seismograph and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Geophysical research in Iceland.

Practicals include solving problems set for each week and exercises in the use of geophysical instruments.  Students write one essay on a selected topic in geophysics.

Basic principles and mathematical methods in thermodynamics,laws of thermodynamics, state functions, Maxwell relations, equilibrium, phase transitions, quantum statistical mechanics, ideal and real gases, specific heat, rate theory, Bose and Fermi distributions.

The objective of the course is to teach the student the basic concepts of thermodynamic systems. The students should also understand different forms of energy, energy transport and conversion from one state to another. The student should be able to calculate the rates of chemical reactions and energy balance.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

Programming in Python (for computations in engineering and science): Main commands and statements (computations, control statements, in- and output), definition and execution of functions, datatypes (numbers, matrices, strings, logical values, records), operations and built-in functions, array and matrix computation, file processing, statistics, graphics. Object-oriented programming: classes, objects, constructors and methods. Concepts associated with design and construction of program systems: Programming environment and practices, design and documentation of function and subroutine libraries, debugging and testing of programmes.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

The course is aimed at students that have already taken a first course in geophysics and have basic knowledge of geophysical exploration and its application.  The course is split in two parts:

1. a) Four to five days of field work at the beginning of autumn term.  Several geophysical methods applied to practical problems.
2. b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computation excises and model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Goal: To teach students the properties of electronic components and circuits, measurement technologies and train them in methods and solutions for electronic circuit design, measurements, research and data acquisition. 

Curriculum: The course covers fundamental issues in electronics, the physics of electronics and electronic components and measurement technology. The curriculum includes theory and practical analysis of AC and dc circuits, diodes and transistors, operational amplifiers and feedback, logic components and digital circuits, digital measurement techniques, amplification and filtering. The course includes twelve laboratory sessions and a project on a microcomputer controlled measurement system. The course concludes with a written exam.

The equations of Laplace and Poisson. Magnetostatics. Induction.  Maxwell's equations. Energy of the electromagnetic field. Poynting's theorem. Electromagnetic waves. Plane waves in dielectric and conducting media, reflection and refraction.  Electromagnetic radiation and scattering. Damping.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

Basic concepts of thermodynamic systems, the zeroth law of thermodynamics. Work, internal energy, heat, enthalpy, the first law of thermodynamics for closed and open systems. Ideal and real gases, equations of state. The second law of thermodynamics, entropy, available energy. Thermodynamic cycles and heat engines, cooling engines and heat pumps. Thermodynamic potentials, Maxwell relations. Mixture of ideal gases. Properties for water and steam. Chemical potentials, chemical reactions of ideal gases, the third law of thermodynamics.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Geological and environmental history of the Earth from the Precambrian, Palaeozoic, Mesozoic, and Cenozoic to present. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, Wilson Cycle, climate history and evolution of life. Fossils, basic principles of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Icehouse and greenhouse Earth and climate change in general. The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the location that will eventually become Iceland. Gradual climate cooling during Cenozoic and implications. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Objectives:   To introduce continuum mechanics, fluid dynamics and heat transfer and their application to problems in physics and geophysics. I. Stress and strain, stress fields, stress tensor, bending of plates, models of material behaviour: elastic, viscous, plastic materials. II. Fluids, viscous fluids, laminar and turbulent flow, equation of continuity, Navier-Stokes equation. III. Heat transfer: Heat conduction, convection, advection and geothermal resources. Examples and problems from various branches of physics will be studied, particularly from geophysics.

Teaching statement: To do well in this course, students should actively participate in the discussions, attend lectures, give student presentations and deliver the problem sets assigned in the course. Students will gain knowledge through the lectures, but it is necessary to do the exercises to understand and train the use of the concepts. The exercises are intergrated in the text of the book, it is recommended to do them while reading the text. Instructors will strive to make the concepts and terminology accessible, but it is expected that students study independently and ask questions if something is unclear. In order to improve the course and its content, it is appreciated that students participate in the course evaluation, both the mid-term and the end of term course evaluation.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

The aim is to introduce students to the disciplines of general oceanography, in particular marine geological, physical and chemical oceanography. To understand how the interactions of processes shape the characteristics of different ocean regions.
The course covers the distribution of land and water, the world oceans and their geomorphology. Instruments and techniques in oceanographic observations. Physical properties of sea water. Energy and water budgets. Distribution of properties in relation to turbulence and diffusion. Introductory dynamical oceanography. Chemical oceanography: Geochemical balance, major and minor elements, dissolved gases. Biogeochemical cycles. Biological processes in relation to the physical and chemical environment. Oceanography of the North Atlantic and Icelandic waters

Students work on the BS-project under the supervision of a teacher.

Geological history of the Precambrian, Palaeozoic and Mesozoic. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, climate history and evolution of life. Fossils and stratigraphy, basic priciples of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Practical work: Written exercises, seminars and reports. Students give seminars and write reports on selected subjects.

Tectonic motions control the nature of the planet we inhabit and the location of continents, mountain ranges, volcanoes, where earthquakes occur and even are important for controlling the Earth's climate. Structural geology and crustal movements in the world, with special emphasis on movements in Iceland. This course introduces the techniques of structural geology through a survey of the mechanics of rock deformation, a survey of the features and geometries of faults and folds, and techniques of strain analysis. Regional structural geology and tectonics are introduced. The subject of the course is active tectonic movements and how this is manifested and recorded in the geological record with emphasis on processes currently active in Iceland. Lectures will be complimented with fieldwork and supportive examples will be given from a global perspective (e.g. compressional tectonics from the Andes and other extensional environments like the East Africa Rift). Methods to describe these processes will be taught and evaluated. Structural geology concepts including elastic, ductile, and brittle behavior of rocks in the crust and mantle will be discussed and discontinuities and brittle fracturing will be addressed. Plate tectonics, plate velocity models, both relative and absolute. Earthquakes. Plate boundary deformation including strike-slip, extensional, and compressive regimes with rifts and rifting structures and folds in addition to mountain building. (If time permits: microstructures, post-rifting and post-seismic movements, Isostasy, vertical crustal movements and sea level, and structural level. measuring crustal movements, GPS-geodesy, levelling, and analysis of seismic stratigraphy (i.e. active source seismic reflection and refraction profiles). Fieldwork will focus on discontinuity analysis and characterisation through a combination of exposure mapping with structural observations coupled with digital elevation (DEMs) model collection using drones and associated analysis to create a coherent assessment of active faults in Southwestern Iceland. Lectures are required as content in the lectures will be tested. Students visiting from abroad in Geology and Geophysics are encouraged to participate in this class as this will be held in English and provide excellent insight into the Iceland Tectonic and Plate Boundary system. 

The aim of the course is to give a comprehensive summary of the environmental change that occurred during the Quaternary period with special reference to Iceland. Contents: The characteristics of the Quaternary and geological evidence for global climatic change. Variations of Earth´s orbital parameters. Dating methods. Glacial debris transport and glacial sedimentation on land and in water. Evidence for climate change in glacier ice and marine and lake sediment. Volcanic activity and the environment. Paleoclimate reconstruction. The glacial and climatic history of Iceland and the North Atlantic Ocean. Grading: Final project 35%, assignments during the semester 30%, presentations 15%, Take home exam 20%. Part of the term project will be a comprehensive search for references to be used by students as they write their term paper and prepare a presentation to be given in class.

Heat budget of the Earth, heat transport to the Earth´s surface. Geothermal systems and their structure, renewability of geothermal systems, methodology in geothermal development, estimation of resource size, fluid origin and chemistry, water-rock interaction, environmental impact of utilization, well testing and well data integration.  The course is taught during 7-week period in the first part of the fall semester.  It consists of lectures, practical, student lectures, student posters, essay and exams.  The course is taught in English.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

The course will focus on the study of sediments and sedimentary rocks, erosion, transport processes and accumulation of sediments, and sedimentary facies and facies associations. Emphasis is placed on linking practical work and lectures. Exercises will be conducted in the field and in the laboratory. Students will be taught to log sedimentary sections and to map sediments and sedimentary rocks, to take samples and perform basic sedimentological analyses of physical properties in the lab.

A 7-week intensive course (first 7 weeks of fall term). 

Taught if sufficient number of students. May be taught as a reading course.

Occurrence of groundwater, the water content of soil, properties and types of aquifers (porosity, retention, yield, storage coefficients; unconfined, confined, leaky, homogeneous, isotropic aquifers). Principles of groundwater flow. Darcy's law, groundwater potential, potentiometric surface, hydraulic conductivity, transmissivity, permeability, determination of hydraulic conductivity in homogeneous and anisotropic aquifers, permeability, flow lines and flow nets, refraction of flow lines, steady and unsteady flow in confined, unconfined and leaky aquifers, general flow equations. Groundwater flow to wells, drawdown and recovery caused by pumping wells, determination of aquifer parameters from time-drawdown data, well loss, capacity and efficiency. Sea-water intrusion in coastal aquifers. Mass transport of solutes by groundwater flow. Quality and pollution of groundwater. Case histories from groundwater studies in Iceland. Numerical models of groundwater flow.   Students carry out an interdisciplinary project on groundwater hydrology and management.

Volcanic eruptions are one of the principal forces that affect and modify the Earth’s surface. The resulting volatile emissions not only replenish and maintain our atmosphere, but are also known to have significant impact atmospheric properties and its circulation. Volcanism has also played a critical role in forming a significant fraction of mineral resources currently exploited by man. As such, volcanic phenomena influence directly or indirectly many (if not all) sub-disciplines of Earth Sciences. Consequently, a basic understanding of how volcanoes work and how they contribute to the earth system cycles is a valuable knowledge to any student in geosciences.

The basic principles of volcanology are covered in this course including the journey of magma from source to surface plus the general processes that control eruptions and dispersal of erupted products. We also cover the principles of eruption monitoring as well as volcano-climate.

Practical sessions will be held weekly and are aimed at solving problems via calculations, data analysis and arguments. One field trip to Reykjanes.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Properties of liquids and gases. Pressure and force fields in liquids at rest, pressure gauges. Equations of motion, continuity, momentum and energy. Bernoulli equation of motion. Dimensional analysis and dynamic similarity. Two dimensional flow, non-viscous fluids, boundary layers theory, laminar and turbulent flow, fluid friction and form drag. Flow of compressible fluids, velocity of sound. Mach number, sound waves, nozzle shape for supersonic speed. Open channel flow. Several experiments are conducted.

Stress and strain tensors, wave-equations for P- and S-waves. Body waves and guided waves. Seismic waves: P-, S-, Rayleigh- and Love-waves. Free oscillations of the Earth. Seismographs, principles and properties. Sources of earthquakes: Focal mechanisms, seismic moment, magnitude scales, energy, frequency spectrum, intensity. Distribution of earthquakes and depths, geological framework. Seismic waves and the internal structure of the Earth.

The course is either tought in a traditional way (lectures, exercises, projects) or as a reading course where the students read textbooks and give a written or oral account of their studies.

The field excursion abroad has the aim to create first-hand experience with respect to the recognition of rock types which do not occur in Iceland and which typically have relatetively high stratigraphic ages (mostly Devonian to Eocene, ca. 400-40 Ma). The excursion will lead us to the "classical square miles in geology" at the northern margin of the Harz Mountains in central Germany. It will encompass the Harz Mountains and its northern foreland, a region listed as one of six UNESCO Global Geoparks in Germany since 2005 (Geopark Harz - Braunschweiger Land - Ostfalen). We will visit natural exposures, old and working quarries, and mines including the visitor mine of Rammelsberg in Goslar which became UNESCO World Heritage Site in 1992.

Igneous and metamorphic rocks such as granites and gneisses, and sedimentary rocks such as sandstones, shales and limestones including reef carbonates will be examined in the field. Karst features and speleothem formation will be explored. Massive Permian rock-salt deposits will be investigated in a mine 670 m below the surface. Eocene lignite deposits will be visited.

This course is only intended for Icelandic undergraduate students.

Students cover all expenses for travel and accommodation including entrance tickets for mines, caves and museum exhibitions apart from the rental of a bus.

The field trip will be from May 18 to 27.

Required equipment:

Slopes can be covered by scree material, and hikes of 5-15 km can be included. Thus, robust shoes are required. In addition, students should bring:

• a field book and pen(s),
• a geological compass,
• a hand lens,
• a scale for photos,
• safety goggles,
• and possibly work gloves.

Temperatures in May can be relatively warm and sun protection (cream, hat, long sleeve shirt) might be useful.

Glaciers are closely connected to the climate system as they both result from it and have impact on it. Glaciers are also important agents of erosion and deposition and the shaping of glacierized landscapes. This course studies glaciers and glacial landscapes with focus on their interaction with both the atmosphere and their substrate. Distribution and classification of glaciers in the world, the formation of glacier ice, glacier mass balance, hydrology, and movement will be discussed, as well as the processes and products of glacial erosion, deposition, and deformation and how they can be used for interpreting past and present glacier state and dynamics. The focus will be on Icelandic glaciers and their foreland geomorphology as signature of past behaviour.

During the course, students will learn terminology and concepts that will equip them to understand and contribute to discussions on the role of glaciers in the climate system in the context of past glacier extent as analysed from the sediment-landform record. Background in high school physics and math is useful, as well as sedimentology and physical geography. At the end of the course, 4-5 day field trip will be run to glaciers on the south coast of Iceland where glacier measurement techniques will be introduced with ablation stakes installed in Sólheimajökull, and students will get hands-on experience in documenting glacial sediments and geomorphology in selected glacier forelands.

Hydrology is the scientific study of earth's water resources. Students will be introduced to the physical and chemical properties of water and the processes responsible for its occurrence, distribution and cycling, with emphasis on the terrestrial phase of the hydrologic cycle as well as the characteristics of the Icelandic water resource. Methods and models used in engineering hydrology and design are introduced, and used to solve projects.

Glaciers in the world are responding fast to climate change, they are therefore important indicators for assessing changes, but have also impact on the climate system through for example albedo feedback and sea level rise. In this course glaciers will be studied, their distribution in the world, how glacier ice is formed from snow, how they move and respond to climate change.  Focus will be on Icelandic glaciers, their energy and mass balance, interaction of geothermal activity and glaciers in Iceland and reoccurring floods, jökulhlaups, from the main ice cap. During the course students will learn terminology and concepts that will equip them to understand and contribute to discussions of climate change and the role of glaciers in the climate system.  Background in high school physics and math is useful, as numerical  problems concerning temperature, energy budget, mass balance and flow of glaciers will be solved in groups. Glacier measurement techniques will be introduced and at the end of the course ablation stakes will be installed in Sólheimajökull on the south coast of Iceland in a two day fielld excursion. Participation in the field trip is mandatory.

The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the geological history of Iceland. Regional stratigraphies. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

Practical work: Weakly written exercises, seminars and reports. Students give talks on selected topics and write reports.

Excursions: Two-day excursion to Snæfellsnes peninsula OR two day-trips to West Iceland and Reykjanes Peninsula.

The aim of the course is to improve the student´s understanding of Earth´s history as well as Earth´s surface processes within a range of geological environments through the Cenozoic.

The basic principles of chemical equilibrium in metamorphic petrology is introduced followed by overview of basic types of metamorphism and metamorphic rocks. Various aspects are covered, including temperature and pressure of metamorphism, time and metamorphism, metamorphic reactions, geothermal gradients, fluid-rock interaction in hydrothermal systems, fluid origin, isotopes, geochemical structure of hydrothermal systems. The course consists of lectures and practices with microscopic examination of metamorphic rocks, calculation of the R-T dependence of metamorphic reactions, short essays and discussion.

Introduction to crystallography and mineralogy. Lectures cover four main fields: 1) Crystallography; 2) Crystal optics; 3) Crystal chemistry; 4) Systematic mineralogy where the students get familiar with the chemical composition and physical properties of the most important rock-forming minerals.

Laboratory work will include exercises with crystal models and optical microscope as well as determination of minerals in hand specimen.

During the course, group projects will also be issued. These projects are optional and the groups present their results at the end of the semester.

Continuum mechanics: Stress and strain, equations of motion. Seismic waves. Maxwell's equations and electromagnetic waves. Plane waves, reflection and refraction. Distributions and Fourier transforms. Fundamental solutions of linear partial differential equation. Waves in homogeneous media. Huygens' principle and Ásgeirsson's mean value theorem. Dispersion, phase and group velocities, Kramers-Kronig equations. The method of stationary phase. Surface waves on liquids.

In this course the student will learn about the origin, generation and evolution of magmas on Earth. A special consideration will be given to processes related to evolution and modification of magma as it passes through the crust.

Lectures will cover physics, chemistry and phase relations of magmas in mantle and crustal environments and igneous thermobarometry.

Practical sessions will cover basic methods of assessing magma origin and evolution. These include phase equilibria/thermodynamics; thermobarometry calculations; and modeling partial melting and fractional crystallization processes. Special emphasis will be on data interpretation and understanding uncertainties during data processing.  
The course runs for 7 weeks in the first half of the spring semester (weeks 1-7) and includes 3 lectures and 4 practical sessions per week.

This course deals with processes of glacial erosion, glacial sedimentation and glacial morphology. It is aimed at undergraduate students interested in physical geography, glacial geology and glaciology. Lectures will concern glacial systems, glacier movements, hydrology, erosion, sediment transport and deposition, glaciotectonic deformations, glacial landforms. The course ends with a 5-day field trip to present glaciers in southern Iceland and formerly glaciated areas in western Iceland, where students get to observe glacial processes and products. Participation in fieldtrip is required for getting course credits.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

Basic concepts in probability and statistics based on univariate calculus. 

Topics: 
Sample space, events, probability, equal probability, independent events, conditional probability, Bayes rule, random variables, distribution, density, joint distribution, independent random variables, condistional distribution, mean, variance, covariance, correlation, law of large numbers, Bernoulli, binomial, Poisson, uniform, exponential and normal random variables. Central limit theorem. Poisson process. Random sample, statistics, the distribution of the sample mean and the sample variance. Point estimate, maximum likelihood estimator, mean square error, bias. Interval estimates and hypotheses testing form normal, binomial and exponential samples. Simple linear regression. Goodness of fit tests, test of independence.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

 This course is an advanced graduate course in tectonics and structural geology, held in English, related to plate boundaries that takes place during 8 weeks in the Spring Semester every other year. This course is a combination of lectures, seminars (i.e. group discussions), and fieldwork using a world-class tectonic and structural laboratory – Iceland! Fieldwork will be a combination of group projects, reporting, and presentations of the results. Tectonics and structural geology controls many important elements of geosystems including: a) global climate (i.e. when the planet is relatively warm or cold), b) geological hazards, where and when and how earthquakes and volcanic eruptions take place, c) location and distribution of natural resources, etc. d) geological engineering problems. This course will explore advanced topics related to these and explore methods including modern field techniques, digital mapping, drone mapping, geophysical prospecting in order to explore structural and tectonic problems. Literature including state of the art peer-reviewed papers will be part of the readings as well as textbook and “classic papers”. Guest lectures, (depending on year), will be given by experts in their field (typically 2 lectures per year) and will involve topics such as: earthquake nucleation and physics-based fault and earthquake modelling, structures and ore bodies, paleomagnetism, paleoseismology, tectonophysical controls on volcanism, igneous intrusions (i.e. dikes and laccoliths). Specific topics that will be addressed yearly are: structural controls on geothermal systems including fluids in faults, structural and tectonic controls of volcanism, tectonic controls of geological hazards, tectonic geomorphology including ideas related to rock and surface uplift, paleoseismology, and neotectonics. Advanced undergraduates are welcome to contact the supervisory Professor if they can demonstrate suitable experience for participating in this exciting course that uses the Plate Boundary of Iceland as part of the learning experience.

The aim of the course is threefold:

• to identify which geological observations and methods are used to decipher Iceland's geological history,
• to analyze the limitations of methods and data
• to identify and explain with examples the main events in Iceland's geological history and the associated geological processes at work. 

Topics covered include the opening of the North Atlantic, the formation of tectonic plate boundaries (the Reykjanes, Kolbeinsey and Ægir ridges). The interaction of the Iceland hotspot with the tectonic plates, rift jumps and the formation of the igneous rock provinces of the North Atlantic will be discussed in the context of the formation of Iceland's bedrock. In addition, the course will address Iceland's past climate, environmental and glacial history, as well as geomorphological evolution. Discussion on the geological history of Iceland is placed in the context with the global conditions that existed when Iceland was being formed and shaped.

Teaching arrangement: This is a 7.5 ECTS course running over 14 weeks. Course material is delivered through lectures, selected readings, and three field trips. Lectures take place once per week (2 × 80 minutes). Attendance on field trips is mandatory.

Teaching statement: To achieve good results in the course, students need to actively participate in lectures and project work. Students gain knowledge in lectures, but it is necessary to do exercises and participate in field trips to increase understanding of concepts and train methods. Teachers will make course concepts and content accessible, but students are expected to study independently and ask questions if something is unclear. Teachers emphasize that students participate in the course evaluation if something needs to be improved. A midterm survey will be reviewed with the students.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Main emphasis is on the differential and integral calculus of functions of a single variable. The systems of real and complex numbers. Least upper bound and greatest lower bound. Natural numbers and induction. Mappings and functions. Sequences and limits. Series and convergence tests. Conditionally convergent series. Limits and continuous functions. Trigonometric functions. Differentiation. Extreme values. The mean value theorem and polynomial approximation. Integration. The fundamental theorem of calculus. Logarithmic and exponential functions, hyperbolic and inverse trigonometric functions. Methods for finding antiderivatives. Real power series. First-order differential equations. Complex valued functions and second-order differential equations.

Introduce students to methods and fundamental laws of mechanics, waves and thermodynamics, to the extent that they can apply their knowledge to solve problems. 

Concepts, units, scales and dimensions.  Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body.  Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound.  Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics.

Note that the textbook is accessible to students via Canvas free of charge.

There are 4 lab sessions with experiments mainly from mechanics, with emphasis on teaching students methods of data collection and data processing. Student hand in a lab report on each experiment. They also hand in a final report from one of these that is intended to look more like a journal article.

The course emphasizes geological processes as a consequence of endogenic processes.

Main topics covered in the course:

• The main features of the Earth’s internal structure, with emphasis on its layering and the properties of individual layers.
• Early hypotheses about continental drift and their development leading to plate tectonics theory, with emphasis on why and how the relative positions of plates and continents are constantly changing.
• The fundamentals of mineral and rock formation and metamorphism.
• Volcanism: causes, distribution, and hazards, with special reference to Iceland.
• Causes of earthquakes and their distribution, different types and behavior of seismic waves, and how this knowledge can be used, for example, to locate and assess the size of earthquakes.
• Structural geology: faults, folds, mountain building, and associated forces.
• Geological time and dating methods, and the geologic time scale, i.e., the arrangement of strata in time and space.
• In addition to general discussion of the course content, special emphasis is placed on the geological and geohistorical formation and position of Iceland.

Teaching Arrangement

The course is 7.5 ECTS and spans 14 weeks. Course content is presented in lectures, selected reading material, practical exercises, and three field trips.

• Lectures are tvice a week inaddtion to on excercise class.
• Field trips: Day trips, usually during the first 4–5 weeks of the semester. Attendance is mandatory. Note field trips can be on weekends.
• Practical exercises: Conducted in classrooms and around the University. Attendance is mandatory.
• Chapter quizzes: Weekly multiple-choice quizzes on textbook chapters. Each quiz is 10 minutes, taken at the beginning of Monday lectures, linked to individual chapters.

Assessment

Assessment is threefold, and all components must be passed with a minimum grade of 5 to pass the course.

• In class exams: 20%
• Field trips and practical exercises: 30%
• Written final exam: 50%

Required Texts and Materials

• Earth – Portrait of a Planet (required). Second half of the book is used in JAR202G.
• Geological Field Techniques (required – pdf provided).
• Compass with clinometer (required).
• Good field notebook (required).
• Hammer, hand lens (recommended).

Teaching Statement

To succeed in this course, students must actively participate in lectures and assignments. Knowledge is gained through lectures and readings, but assignments and field trips are essential to deepen understanding and practice methods. Teachers will make key concepts and materials accessible, but students are expected to learn independently and ask questions if unclear. Teachers emphasize participation in course evaluations to address improvements. The midterm survey will be reviewed with students after completion.

Code of Conduct

Great emphasis is placed on honest academic work in accordance with the University of Iceland’s Code of Ethics:
https://www.hi.is/haskolinn/sidareglur
If a student is found guilty of misconduct in exams or coursework, action will be taken as outlined in the University’s regulations:
https://ugla.hi.is/kennsluskra/index.php?tab=skoli&chapter=content&id=46779

Turnitin

Assignments in this course will be checked using Turnitin.

Artificial Intelligence

Use of AI in studies at the University of Iceland is governed by university guidelines:
https://gervigreind.hi.is/
In this course, the use of AI in assignments and/or exams is not permitted unless explicitly allowed by the instructors. Any uncertainty regarding AI use must be clarified with the course coordinator.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Tutor classes for Earth Science students

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Emphasis is laid on the theoretical aspects of the material. The aim is that the students acquire understanding of fundamental concepts and are able to use them, both in theoretical consideration and in calculations. Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobian matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flows. Cylindrical and spherical coordinates. Taylor polynomials. Extrema and classification of stationary points. Extrema with constraints. Implicit functions and local inverses. Line integrals and potential functions. Proper and improper multiple integrals. Change of variables in multiple integrals. Simply connected regions. Integration on surfaces. Theorems of Green, Stokes and Gauss.

Introduction to electrodynamics in material; from insulators to superconductors.  Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics.

There are four 4 hour lab sessions and two 3 hour sessions, from optics and electromagnetism. Students hand in a lab report on each experiment. They also hand in a final report from one of the 4 hour experiments that is intended to look more like a journal article.

This course focuses on the Earth Surface processes, specifically those that contribute to the formation of various landforms and landscapes and how these landforms evolve and erode over time and space. Emphasis is placed on enabling students to discuss these geological processes using geological terminology in both Icelandic and English.

Key topics include:

• Basic sedimentology, with a focus on changes in grain size, distribution, and texture of rock particles during transport by running water, glaciers, and wind.
• Earth's water cycle and its significant role in shaping terrestrial landscapes through weathering, erosion, and deposition of rock material.
• Running water as the most influential agent in shaping Earth's land surfaces through both erosion and transport of rock debris.
• Coastal dynamics and factors influencing shoreline development, highlighting the ongoing changes, fast and slow, at the land-sea boundary.
• Groundwater's role in land formation, its importance for drinking water supply, and measures to protect this vital resource.
• The Earth's atmospheric circulation, its influence on precipitation patterns, and the distribution of arid and vegetative areas.
• Erosional and depositional processes and their role in landform development in Iceland, focusing on glaciation and its history, especially during the last ice age.
• Discussion of Earth's inorganic and organic resources, their formation, distribution, extraction, usage, disposal, renewal, and recycling.
• Special emphasis is placed on relating the theoretical aspects of the course to Iceland by exploring relevant local examples.

Teaching Arrangement

The course is worth 7.5 ECTS and spans 14 weeks. Material is presented through lectures, selected readings, and a 5-day field trip to South Iceland and the Westman Islands. The primary purpose of the field trip is to provide students with direct experience of the processes and landforms covered in the course. The field trip takes place immediately after the spring exams and is mandatory. Students must cover their own meal expenses during the trip. Weekly multiple-choice exams related to textbook chapters are assigned.

Teaching Statement

For students to succeed in this course, active participation in lectures and assignments is key. Students will gain knowledge through lectures and reading material but completing assignments and attending field trips are essential for deepening understanding of key concepts and methods. Instructors will make course concepts accessible, but students are expected to learn independently and ask questions if anything is unclear. Instructors emphasize the importance of student feedback through course evaluations to address areas for improvement, with a mid-term evaluation reviewed with students.

Assessment

The course assessment is three-fold, and all parts must be completed with a minimum grade of 5 to pass the course.

• Multiple choice exams: 25%

• Field trip journal: 15%
• Written final exam: 60%

Learning Outcomes:

Upon completing the course, students should be able to:

• Use geological terminology to discuss the natural environment of the land.
• Explain the role of Earth's exogenic forces in the ever-changing appearance of its land surface.
• Provide examples of how the effects of these exogenic forces vary across time and space.
• Analyze the role of exogenic forces in shaping individual landforms and landscapes.
• Identify individual landforms and landscapes and link them to one or more exogenic processes.
• Analyze composite evidence of exogenic processes and use that analysis to describe the sequence of events, in time and space, that created specific landforms and landscapes.
• Read geological maps that show surface deposits.
• Record and manage their own observations in a field notebook.

An introduction to the physics of the Earth. Origin and age of the Earth. Dating with radioactive elements. Gravity, shape and rotation of the Earth, the geomagnetic field, magnetic anomalies, palaeomagnetism, electric conductivity. Earthquakes, seismograph and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Geophysical research in Iceland.

Practicals include solving problems set for each week and exercises in the use of geophysical instruments.  Students write one essay on a selected topic in geophysics.

Basic principles and mathematical methods in thermodynamics,laws of thermodynamics, state functions, Maxwell relations, equilibrium, phase transitions, quantum statistical mechanics, ideal and real gases, specific heat, rate theory, Bose and Fermi distributions.

The objective of the course is to teach the student the basic concepts of thermodynamic systems. The students should also understand different forms of energy, energy transport and conversion from one state to another. The student should be able to calculate the rates of chemical reactions and energy balance.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

Programming in Python (for computations in engineering and science): Main commands and statements (computations, control statements, in- and output), definition and execution of functions, datatypes (numbers, matrices, strings, logical values, records), operations and built-in functions, array and matrix computation, file processing, statistics, graphics. Object-oriented programming: classes, objects, constructors and methods. Concepts associated with design and construction of program systems: Programming environment and practices, design and documentation of function and subroutine libraries, debugging and testing of programmes.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

The course is aimed at students that have already taken a first course in geophysics and have basic knowledge of geophysical exploration and its application.  The course is split in two parts:

1. a) Four to five days of field work at the beginning of autumn term.  Several geophysical methods applied to practical problems.
2. b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computation excises and model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Goal: To teach students the properties of electronic components and circuits, measurement technologies and train them in methods and solutions for electronic circuit design, measurements, research and data acquisition. 

Curriculum: The course covers fundamental issues in electronics, the physics of electronics and electronic components and measurement technology. The curriculum includes theory and practical analysis of AC and dc circuits, diodes and transistors, operational amplifiers and feedback, logic components and digital circuits, digital measurement techniques, amplification and filtering. The course includes twelve laboratory sessions and a project on a microcomputer controlled measurement system. The course concludes with a written exam.

The equations of Laplace and Poisson. Magnetostatics. Induction.  Maxwell's equations. Energy of the electromagnetic field. Poynting's theorem. Electromagnetic waves. Plane waves in dielectric and conducting media, reflection and refraction.  Electromagnetic radiation and scattering. Damping.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

Basic concepts of thermodynamic systems, the zeroth law of thermodynamics. Work, internal energy, heat, enthalpy, the first law of thermodynamics for closed and open systems. Ideal and real gases, equations of state. The second law of thermodynamics, entropy, available energy. Thermodynamic cycles and heat engines, cooling engines and heat pumps. Thermodynamic potentials, Maxwell relations. Mixture of ideal gases. Properties for water and steam. Chemical potentials, chemical reactions of ideal gases, the third law of thermodynamics.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Geological and environmental history of the Earth from the Precambrian, Palaeozoic, Mesozoic, and Cenozoic to present. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, Wilson Cycle, climate history and evolution of life. Fossils, basic principles of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Icehouse and greenhouse Earth and climate change in general. The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the location that will eventually become Iceland. Gradual climate cooling during Cenozoic and implications. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

The course is devoted to theoretical foundations of quantum mechanics. 

Prelude to quantum physics. Wave functions and probability, Schrödinger's equation, momentum and the uncertainty principle, stationary states, one-dimensional quantum systems. Schrödinger's equation in spherical coordinates, the hydrogen atom, angular momentum and spin. Identical particles and the Pauli principle. Two-level systems, emission and absorbtion of radiation.

Objectives:   To introduce continuum mechanics, fluid dynamics and heat transfer and their application to problems in physics and geophysics. I. Stress and strain, stress fields, stress tensor, bending of plates, models of material behaviour: elastic, viscous, plastic materials. II. Fluids, viscous fluids, laminar and turbulent flow, equation of continuity, Navier-Stokes equation. III. Heat transfer: Heat conduction, convection, advection and geothermal resources. Examples and problems from various branches of physics will be studied, particularly from geophysics.

Teaching statement: To do well in this course, students should actively participate in the discussions, attend lectures, give student presentations and deliver the problem sets assigned in the course. Students will gain knowledge through the lectures, but it is necessary to do the exercises to understand and train the use of the concepts. The exercises are intergrated in the text of the book, it is recommended to do them while reading the text. Instructors will strive to make the concepts and terminology accessible, but it is expected that students study independently and ask questions if something is unclear. In order to improve the course and its content, it is appreciated that students participate in the course evaluation, both the mid-term and the end of term course evaluation.

A full semester course – 14 weeks.

a) One week field work at the beginning of autumn term.  Several geophysical methods applied to a practical problem.

b) Geophysical exploration methods and their application in the search for energy resources and minerals. Theoretical basis, instruments, measurement procedures, data processing and interpretation. Seismic reflection and refraction, gravity, magnetics, electrical methods, borehole logging. Practical work includes computations, model experiments.  Interpretation and preparation of report on field work done at beginning of course.

Taught every odd year.

Elementary atmospheric thermodynamics, radiation and motion. Atmospheric general circulation, atmosphere/ocean interaction, the role of polar areas in the atmospheric circulation, climate fluctuations. Introduction to recent research. Students deliver a written report on a selected topic.

The aim is to introduce students to the disciplines of general oceanography, in particular marine geological, physical and chemical oceanography. To understand how the interactions of processes shape the characteristics of different ocean regions.
The course covers the distribution of land and water, the world oceans and their geomorphology. Instruments and techniques in oceanographic observations. Physical properties of sea water. Energy and water budgets. Distribution of properties in relation to turbulence and diffusion. Introductory dynamical oceanography. Chemical oceanography: Geochemical balance, major and minor elements, dissolved gases. Biogeochemical cycles. Biological processes in relation to the physical and chemical environment. Oceanography of the North Atlantic and Icelandic waters

Students work on the BS-project under the supervision of a teacher.

Geological history of the Precambrian, Palaeozoic and Mesozoic. Basic principles of stratigraphy, time and geological age determinations. Plate tectonics and supercontinents, regional stratigraphy, climate history and evolution of life. Fossils and stratigraphy, basic priciples of paleontology, avenues of evolution and mass extinctions. Fossils and environment. Practical work: Written exercises, seminars and reports. Students give seminars and write reports on selected subjects.

Tectonic motions control the nature of the planet we inhabit and the location of continents, mountain ranges, volcanoes, where earthquakes occur and even are important for controlling the Earth's climate. Structural geology and crustal movements in the world, with special emphasis on movements in Iceland. This course introduces the techniques of structural geology through a survey of the mechanics of rock deformation, a survey of the features and geometries of faults and folds, and techniques of strain analysis. Regional structural geology and tectonics are introduced. The subject of the course is active tectonic movements and how this is manifested and recorded in the geological record with emphasis on processes currently active in Iceland. Lectures will be complimented with fieldwork and supportive examples will be given from a global perspective (e.g. compressional tectonics from the Andes and other extensional environments like the East Africa Rift). Methods to describe these processes will be taught and evaluated. Structural geology concepts including elastic, ductile, and brittle behavior of rocks in the crust and mantle will be discussed and discontinuities and brittle fracturing will be addressed. Plate tectonics, plate velocity models, both relative and absolute. Earthquakes. Plate boundary deformation including strike-slip, extensional, and compressive regimes with rifts and rifting structures and folds in addition to mountain building. (If time permits: microstructures, post-rifting and post-seismic movements, Isostasy, vertical crustal movements and sea level, and structural level. measuring crustal movements, GPS-geodesy, levelling, and analysis of seismic stratigraphy (i.e. active source seismic reflection and refraction profiles). Fieldwork will focus on discontinuity analysis and characterisation through a combination of exposure mapping with structural observations coupled with digital elevation (DEMs) model collection using drones and associated analysis to create a coherent assessment of active faults in Southwestern Iceland. Lectures are required as content in the lectures will be tested. Students visiting from abroad in Geology and Geophysics are encouraged to participate in this class as this will be held in English and provide excellent insight into the Iceland Tectonic and Plate Boundary system. 

The aim of the course is to give a comprehensive summary of the environmental change that occurred during the Quaternary period with special reference to Iceland. Contents: The characteristics of the Quaternary and geological evidence for global climatic change. Variations of Earth´s orbital parameters. Dating methods. Glacial debris transport and glacial sedimentation on land and in water. Evidence for climate change in glacier ice and marine and lake sediment. Volcanic activity and the environment. Paleoclimate reconstruction. The glacial and climatic history of Iceland and the North Atlantic Ocean. Grading: Final project 35%, assignments during the semester 30%, presentations 15%, Take home exam 20%. Part of the term project will be a comprehensive search for references to be used by students as they write their term paper and prepare a presentation to be given in class.

Heat budget of the Earth, heat transport to the Earth´s surface. Geothermal systems and their structure, renewability of geothermal systems, methodology in geothermal development, estimation of resource size, fluid origin and chemistry, water-rock interaction, environmental impact of utilization, well testing and well data integration.  The course is taught during 7-week period in the first part of the fall semester.  It consists of lectures, practical, student lectures, student posters, essay and exams.  The course is taught in English.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

The course will focus on the study of sediments and sedimentary rocks, erosion, transport processes and accumulation of sediments, and sedimentary facies and facies associations. Emphasis is placed on linking practical work and lectures. Exercises will be conducted in the field and in the laboratory. Students will be taught to log sedimentary sections and to map sediments and sedimentary rocks, to take samples and perform basic sedimentological analyses of physical properties in the lab.

A 7-week intensive course (first 7 weeks of fall term). 

Taught if sufficient number of students. May be taught as a reading course.

Occurrence of groundwater, the water content of soil, properties and types of aquifers (porosity, retention, yield, storage coefficients; unconfined, confined, leaky, homogeneous, isotropic aquifers). Principles of groundwater flow. Darcy's law, groundwater potential, potentiometric surface, hydraulic conductivity, transmissivity, permeability, determination of hydraulic conductivity in homogeneous and anisotropic aquifers, permeability, flow lines and flow nets, refraction of flow lines, steady and unsteady flow in confined, unconfined and leaky aquifers, general flow equations. Groundwater flow to wells, drawdown and recovery caused by pumping wells, determination of aquifer parameters from time-drawdown data, well loss, capacity and efficiency. Sea-water intrusion in coastal aquifers. Mass transport of solutes by groundwater flow. Quality and pollution of groundwater. Case histories from groundwater studies in Iceland. Numerical models of groundwater flow.   Students carry out an interdisciplinary project on groundwater hydrology and management.

Volcanic eruptions are one of the principal forces that affect and modify the Earth’s surface. The resulting volatile emissions not only replenish and maintain our atmosphere, but are also known to have significant impact atmospheric properties and its circulation. Volcanism has also played a critical role in forming a significant fraction of mineral resources currently exploited by man. As such, volcanic phenomena influence directly or indirectly many (if not all) sub-disciplines of Earth Sciences. Consequently, a basic understanding of how volcanoes work and how they contribute to the earth system cycles is a valuable knowledge to any student in geosciences.

The basic principles of volcanology are covered in this course including the journey of magma from source to surface plus the general processes that control eruptions and dispersal of erupted products. We also cover the principles of eruption monitoring as well as volcano-climate.

Practical sessions will be held weekly and are aimed at solving problems via calculations, data analysis and arguments. One field trip to Reykjanes.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Properties of liquids and gases. Pressure and force fields in liquids at rest, pressure gauges. Equations of motion, continuity, momentum and energy. Bernoulli equation of motion. Dimensional analysis and dynamic similarity. Two dimensional flow, non-viscous fluids, boundary layers theory, laminar and turbulent flow, fluid friction and form drag. Flow of compressible fluids, velocity of sound. Mach number, sound waves, nozzle shape for supersonic speed. Open channel flow. Several experiments are conducted.

Stress and strain tensors, wave-equations for P- and S-waves. Body waves and guided waves. Seismic waves: P-, S-, Rayleigh- and Love-waves. Free oscillations of the Earth. Seismographs, principles and properties. Sources of earthquakes: Focal mechanisms, seismic moment, magnitude scales, energy, frequency spectrum, intensity. Distribution of earthquakes and depths, geological framework. Seismic waves and the internal structure of the Earth.

The course is either tought in a traditional way (lectures, exercises, projects) or as a reading course where the students read textbooks and give a written or oral account of their studies.

The field excursion abroad has the aim to create first-hand experience with respect to the recognition of rock types which do not occur in Iceland and which typically have relatetively high stratigraphic ages (mostly Devonian to Eocene, ca. 400-40 Ma). The excursion will lead us to the "classical square miles in geology" at the northern margin of the Harz Mountains in central Germany. It will encompass the Harz Mountains and its northern foreland, a region listed as one of six UNESCO Global Geoparks in Germany since 2005 (Geopark Harz - Braunschweiger Land - Ostfalen). We will visit natural exposures, old and working quarries, and mines including the visitor mine of Rammelsberg in Goslar which became UNESCO World Heritage Site in 1992.

Igneous and metamorphic rocks such as granites and gneisses, and sedimentary rocks such as sandstones, shales and limestones including reef carbonates will be examined in the field. Karst features and speleothem formation will be explored. Massive Permian rock-salt deposits will be investigated in a mine 670 m below the surface. Eocene lignite deposits will be visited.

This course is only intended for Icelandic undergraduate students.

Students cover all expenses for travel and accommodation including entrance tickets for mines, caves and museum exhibitions apart from the rental of a bus.

The field trip will be from May 18 to 27.

Required equipment:

Slopes can be covered by scree material, and hikes of 5-15 km can be included. Thus, robust shoes are required. In addition, students should bring:

• a field book and pen(s),
• a geological compass,
• a hand lens,
• a scale for photos,
• safety goggles,
• and possibly work gloves.

Temperatures in May can be relatively warm and sun protection (cream, hat, long sleeve shirt) might be useful.

Glaciers are closely connected to the climate system as they both result from it and have impact on it. Glaciers are also important agents of erosion and deposition and the shaping of glacierized landscapes. This course studies glaciers and glacial landscapes with focus on their interaction with both the atmosphere and their substrate. Distribution and classification of glaciers in the world, the formation of glacier ice, glacier mass balance, hydrology, and movement will be discussed, as well as the processes and products of glacial erosion, deposition, and deformation and how they can be used for interpreting past and present glacier state and dynamics. The focus will be on Icelandic glaciers and their foreland geomorphology as signature of past behaviour.

During the course, students will learn terminology and concepts that will equip them to understand and contribute to discussions on the role of glaciers in the climate system in the context of past glacier extent as analysed from the sediment-landform record. Background in high school physics and math is useful, as well as sedimentology and physical geography. At the end of the course, 4-5 day field trip will be run to glaciers on the south coast of Iceland where glacier measurement techniques will be introduced with ablation stakes installed in Sólheimajökull, and students will get hands-on experience in documenting glacial sediments and geomorphology in selected glacier forelands.

Hydrology is the scientific study of earth's water resources. Students will be introduced to the physical and chemical properties of water and the processes responsible for its occurrence, distribution and cycling, with emphasis on the terrestrial phase of the hydrologic cycle as well as the characteristics of the Icelandic water resource. Methods and models used in engineering hydrology and design are introduced, and used to solve projects.

Glaciers in the world are responding fast to climate change, they are therefore important indicators for assessing changes, but have also impact on the climate system through for example albedo feedback and sea level rise. In this course glaciers will be studied, their distribution in the world, how glacier ice is formed from snow, how they move and respond to climate change.  Focus will be on Icelandic glaciers, their energy and mass balance, interaction of geothermal activity and glaciers in Iceland and reoccurring floods, jökulhlaups, from the main ice cap. During the course students will learn terminology and concepts that will equip them to understand and contribute to discussions of climate change and the role of glaciers in the climate system.  Background in high school physics and math is useful, as numerical  problems concerning temperature, energy budget, mass balance and flow of glaciers will be solved in groups. Glacier measurement techniques will be introduced and at the end of the course ablation stakes will be installed in Sólheimajökull on the south coast of Iceland in a two day fielld excursion. Participation in the field trip is mandatory.

The geological history of Earth during the Cenozoic Era in general, and with special emphasis on the opening of the North Atlantic Ocean and the geological history of Iceland. Regional stratigraphies. Fossil evidence on Cenozoic evolution of life, with emphasis on evolution of mammals in general and primates and Man in particular. This includes topics like evolution of environments, continental rift and mountain building, evolution of life, speciation, biodiversity and mass extinctions. Quaternary glacial- and climate history.

Practical work: Weakly written exercises, seminars and reports. Students give talks on selected topics and write reports.

Excursions: Two-day excursion to Snæfellsnes peninsula OR two day-trips to West Iceland and Reykjanes Peninsula.

The aim of the course is to improve the student´s understanding of Earth´s history as well as Earth´s surface processes within a range of geological environments through the Cenozoic.

The basic principles of chemical equilibrium in metamorphic petrology is introduced followed by overview of basic types of metamorphism and metamorphic rocks. Various aspects are covered, including temperature and pressure of metamorphism, time and metamorphism, metamorphic reactions, geothermal gradients, fluid-rock interaction in hydrothermal systems, fluid origin, isotopes, geochemical structure of hydrothermal systems. The course consists of lectures and practices with microscopic examination of metamorphic rocks, calculation of the R-T dependence of metamorphic reactions, short essays and discussion.

Introduction to crystallography and mineralogy. Lectures cover four main fields: 1) Crystallography; 2) Crystal optics; 3) Crystal chemistry; 4) Systematic mineralogy where the students get familiar with the chemical composition and physical properties of the most important rock-forming minerals.

Laboratory work will include exercises with crystal models and optical microscope as well as determination of minerals in hand specimen.

During the course, group projects will also be issued. These projects are optional and the groups present their results at the end of the semester.

Continuum mechanics: Stress and strain, equations of motion. Seismic waves. Maxwell's equations and electromagnetic waves. Plane waves, reflection and refraction. Distributions and Fourier transforms. Fundamental solutions of linear partial differential equation. Waves in homogeneous media. Huygens' principle and Ásgeirsson's mean value theorem. Dispersion, phase and group velocities, Kramers-Kronig equations. The method of stationary phase. Surface waves on liquids.

In this course the student will learn about the origin, generation and evolution of magmas on Earth. A special consideration will be given to processes related to evolution and modification of magma as it passes through the crust.

Lectures will cover physics, chemistry and phase relations of magmas in mantle and crustal environments and igneous thermobarometry.

Practical sessions will cover basic methods of assessing magma origin and evolution. These include phase equilibria/thermodynamics; thermobarometry calculations; and modeling partial melting and fractional crystallization processes. Special emphasis will be on data interpretation and understanding uncertainties during data processing.  
The course runs for 7 weeks in the first half of the spring semester (weeks 1-7) and includes 3 lectures and 4 practical sessions per week.

This course deals with processes of glacial erosion, glacial sedimentation and glacial morphology. It is aimed at undergraduate students interested in physical geography, glacial geology and glaciology. Lectures will concern glacial systems, glacier movements, hydrology, erosion, sediment transport and deposition, glaciotectonic deformations, glacial landforms. The course ends with a 5-day field trip to present glaciers in southern Iceland and formerly glaciated areas in western Iceland, where students get to observe glacial processes and products. Participation in fieldtrip is required for getting course credits.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

Basic concepts in probability and statistics based on univariate calculus. 

Topics: 
Sample space, events, probability, equal probability, independent events, conditional probability, Bayes rule, random variables, distribution, density, joint distribution, independent random variables, condistional distribution, mean, variance, covariance, correlation, law of large numbers, Bernoulli, binomial, Poisson, uniform, exponential and normal random variables. Central limit theorem. Poisson process. Random sample, statistics, the distribution of the sample mean and the sample variance. Point estimate, maximum likelihood estimator, mean square error, bias. Interval estimates and hypotheses testing form normal, binomial and exponential samples. Simple linear regression. Goodness of fit tests, test of independence.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

 This course is an advanced graduate course in tectonics and structural geology, held in English, related to plate boundaries that takes place during 8 weeks in the Spring Semester every other year. This course is a combination of lectures, seminars (i.e. group discussions), and fieldwork using a world-class tectonic and structural laboratory – Iceland! Fieldwork will be a combination of group projects, reporting, and presentations of the results. Tectonics and structural geology controls many important elements of geosystems including: a) global climate (i.e. when the planet is relatively warm or cold), b) geological hazards, where and when and how earthquakes and volcanic eruptions take place, c) location and distribution of natural resources, etc. d) geological engineering problems. This course will explore advanced topics related to these and explore methods including modern field techniques, digital mapping, drone mapping, geophysical prospecting in order to explore structural and tectonic problems. Literature including state of the art peer-reviewed papers will be part of the readings as well as textbook and “classic papers”. Guest lectures, (depending on year), will be given by experts in their field (typically 2 lectures per year) and will involve topics such as: earthquake nucleation and physics-based fault and earthquake modelling, structures and ore bodies, paleomagnetism, paleoseismology, tectonophysical controls on volcanism, igneous intrusions (i.e. dikes and laccoliths). Specific topics that will be addressed yearly are: structural controls on geothermal systems including fluids in faults, structural and tectonic controls of volcanism, tectonic controls of geological hazards, tectonic geomorphology including ideas related to rock and surface uplift, paleoseismology, and neotectonics. Advanced undergraduates are welcome to contact the supervisory Professor if they can demonstrate suitable experience for participating in this exciting course that uses the Plate Boundary of Iceland as part of the learning experience.

The aim of the course is threefold:

• to identify which geological observations and methods are used to decipher Iceland's geological history,
• to analyze the limitations of methods and data
• to identify and explain with examples the main events in Iceland's geological history and the associated geological processes at work. 

Topics covered include the opening of the North Atlantic, the formation of tectonic plate boundaries (the Reykjanes, Kolbeinsey and Ægir ridges). The interaction of the Iceland hotspot with the tectonic plates, rift jumps and the formation of the igneous rock provinces of the North Atlantic will be discussed in the context of the formation of Iceland's bedrock. In addition, the course will address Iceland's past climate, environmental and glacial history, as well as geomorphological evolution. Discussion on the geological history of Iceland is placed in the context with the global conditions that existed when Iceland was being formed and shaped.

Teaching arrangement: This is a 7.5 ECTS course running over 14 weeks. Course material is delivered through lectures, selected readings, and three field trips. Lectures take place once per week (2 × 80 minutes). Attendance on field trips is mandatory.

Teaching statement: To achieve good results in the course, students need to actively participate in lectures and project work. Students gain knowledge in lectures, but it is necessary to do exercises and participate in field trips to increase understanding of concepts and train methods. Teachers will make course concepts and content accessible, but students are expected to study independently and ask questions if something is unclear. Teachers emphasize that students participate in the course evaluation if something needs to be improved. A midterm survey will be reviewed with the students.