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.

The Java programming language will be used to introduce basic practices in computer programming. Practice in programming is scheduled throughout the semester. An emphasis is placed on logical methods for writing program and good documentation. Main ideas related to computers and programming. Classes, objects and methods. Control statements. Strings and arrays, operations and built-in functons. Input and output. Inheritance. Ideas relatied to system design and good practices for program writing. Iteration and recursion. Searching and Sorting.

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.

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.

Basics of linear algebra over the reals with emphasis on the theoretical side. 

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 nullspace. 
The dot product, length and angle measures.  Volumes in higher dimensions 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.

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.

Introduction to the theory of Special Relativity and some basic concepts of General Relativity.

The need for Special Relativity (light propagation and key historical experiments). Einstein's principle of relativity, time dilation and length contraction. The geometry of spacetime (Minkowski space), the Lorentz transformation and causality. Kinematics, dynamics and electromagnetism in Special Relativity.
A brief introduction to General Relativity.

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.

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.

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.

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.

Python tools related to data analysis and plotting. Mathematical concepts such as vectors, matrices, differential operators in three dimensions, coordinate transformations, partial differential equations and Fourier series and their relation to undergraduate courses in physics and engineering. We will emphasize applications and problem solving.

This is an extension of the course "Probability and Statistics" STÆ203G. The basic concepts of probability are considered in more detail with emphasis on definitions and proofs. The course is a preparation for the two M-courses in probability and the two M-courses in statistics that are taught alternately every other year.

Topics beyond those discussed in the probability part of STÆ203G:

Kolmogorov's definition. Proofs of propositions on compound events and conditional probability. Proofs for discrete and continuous variables of propositions on expectation, variance, covariance, correlation, and conditional expectation and variance. Proofs of propositions for Bernoulli, binomial, Poisson, geometric, uniform, exponential, and gamma variables. Proof of the tail-summing proposition for expectation and the application to the geometric variable. Proof of the proposition on memoryless and exponential variables. Derivation of the distribution of sums of independent variables such as binomial, Poisson, normal, and gamma variables. Probability and moment generating functions.

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.

The course is an introduction to three important tools of applied mathematics, namely ordinary differential equations, Fourier-series and partial differential equations.  Some basic theoretical properties are proved and solution methods presented. 

Subject matter: Ordinary differential equations: linear differential equations of order n, the Cauchy problem, Picard's existence theorem, solution by power series and equations with singular points.  Fourier series: convergence point-wise, uniformly and in the mean-square, Parseval's equation.  Partial differential equations:

the heat equation and the wave equation solved on a finite interval by separation of variables and Fourier series and their solutions compared, the Dirichlet problem for the Laplace equation on the rectangle and the disc, the Poisson integral formula.

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.

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.

The course is devoted to theoretical foundations of wave and quantum mechanics. The main concepts characterizing classical waves, such as wave equation, plane waves, wavepackets and phase and group velocity are discussed and then, after the introduction of the concept of particle-wave dualism are used to describe the properties of the de Broglie material waves corresponding to quantum particles. Dynamic and stationary Schrodinger equations are introduced, and their solutions for a set of physically important particular cases, including quantum tunneling, quantum potential well, quantum harmonic oscillator and Coulomb potential are analyzed in all necessary detail. The last part of the course is devoted to the quantum description of spin.

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.

Python tools related to data analysis and manipulation of graphs. Differential equations and their use in the description of physical systems. Partial differential equations and boundary value problems. Special functions and their relation to important problems in physics. We will emphasize applications and problem solving.

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.

Introduction to atomic and molecular physics and modern optics. Electronic structure of atoms, the periodic table, chemical bonds and molecules, rotational and vibrational states, interaction between light and matter, symmetry and selection rules, polarisation, resonators and interferometers, atomic and molecular spectroscopy, optical amplification, lasers. The course includes three laboratory exercises.

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.

The course is devoted to the foundations of nuclear and elementary particle physics. It consists of the lectures on the corresponding theory and a laboratory of 2 week duration. In theoretical part students learn about basic ideas of nuclear physics, such as simplest nuclear models, basics of the scattering physics, types of elementary particles and their fundamental interactions. After that basics of the relativistic wave equations are introduced. The cases of Klein-Gordon, Higgs, and Dirac equations are considered. Higgs equation is used to introduce the fundamental concept of spontaneous symmetry breaking, necessary for the understanding of the appearance of a Higgs boson.  Solution of the Dirac equation for free particles is analyzed, and related fundamental concepts of antiparticles, helicity and chirality are considered in detail. 

The postulates and formalism of quantum mechanics. One-dimensional systems. Angular momentum, spin, two level systems. Particles in a central potential, the hydrogen atom. Approximation methods. Time independent and time dependent perturbation. Scattering.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Presentation of important techniques used in experimental physics and of various phenomena related to the subject matter of the second and third year of the Physics curriculum. Six extensive experiments are made, most of which are related to active research in experimental physics at the Science Institute of the University of Iceland.  The course emphasizes independence in carrying out the experiments, data analysis and literature search.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 8 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Seminar course on topics of current interest in astrophysics and cosmology.

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

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.

Selected topics in theoretical and experimental physics. Each student gives one lecture on a topic of his or her choice.

Introduction to how numerical analysis is used to explore the properties of physical system. Programming environment and graphical representation.  The application of functional bases to solve simple models in quantum and statistical physics. Parallel processing on clusters.  Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing

Identical particles, second quantization. Density operators, pure and mixed quantum states. Symmetries in quantum mechanics, the rotation group, addition of angular momenta, tensor operators, Wigner-Eckardt theorem. Interaction of atoms and radiation, spontaneous emission. Feynman path integrals.

The basis of the atomic theory. Stoichiometry. Types of chemical reactions and solution stoichiometry. Properties of gases. Chemical equilibrium. Acids and bases. Applications of aqueous equilibria. Chemical thermodynamics. Enthropy, free energy and equilibrium. Electrochemistry. Chemical kinetics. Physical properties of solutions.

An introduction to the physics of the Earth. The course should be suitable as a first course for those majoring in geophysics and for geology students wanting to become familiar with the subject. Gravity, shape and rotation of the Earth, gravity anomalies. The geomagnetic field, magnetic anomalies, palaeomagnetism. Earthquakes and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Origin and age of the Earth. Dating with radioactive elements. Geophysics of Iceland, introduction to geophysical research in Iceland.

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

Taught if sufficient number of students. May be taugth 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.

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.

This course is only for exchange students. It is taught with JEÐ301G tektonik. The subject of the course is active tectonic movements with emphasis on processes currently active in Iceland. Theory of plate tectonics, plate velocity models, both relative and absolute. Elastic and ductile behaviour of rocks in the crust and mantle. Brittle fracturing. Plate boundary deformation. Rifts and rifting structures. Transcurrent faulting and associated structures. Earthquakes and faulting. Measuring crustal movements, GPS-geodesy, levelling, SAR-interferometry, tilt- and strainmeters. A one-day field project will be carried out in an active area. Additionally, one day field trip to the plate boundary areas of SW-Iceland. Five home exercises are assigned. Solutions and report are to be handed in. A 3-hour written exam will be held at the end of the semester. Reports of exercises and field project are obligatory and count 20% towards a grade.

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.

Complex numbers and the topology of the complex plane. Sequences and series of complex numbers. Differentiable and holomorphic functions. Sequences and series of functions; power series. Path integration and primitives. The exponential function and related functions. Winding numbers. The Cauchy theorem, the integral formula of Cauchy and consequences. The identity theorem, the open mapping theorem and the maximum principle. Laurent series, isolated singularities and their classification. The theorem of residues and residue calculus. The argument principle and Rouché's theorem. Connections with real analysis: The Cauchy-Riemann equations, harmonic functions and the integral formulas of Poisson and Schwarz. Holomorphic functions defined by integrals (e. g. the Laplace transformation). Conformal mapping and the Riemann mapping theorem.

The object of the course is to give a firm and rigorous foundation for more advanced studies in partial differential equations. Contents: first order equations; the Cauchy-Kowalevski theorem; techniques of analysis (Lebesgue-integral, convolutions, Fourier-transform); distributions; fundamental solutions; the Laplace operator; the heat operator.  The course is mainly intended for postgraduate students with a good background in analysis.

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.

An introduction to astrophysical problems with emphasis on underlying physical principles. -- The nature of stars. Equations of state, stellar energy generation, radiative transfer. Stellar structure and evolution. Gravitational collapse and supernova explosions. Physics of white dwarfs, neutron stars and black holes. Compact binary systems. X-ray sources. Pulsars. Galaxies, their structure, formation and evolution. Active galaxies. The interstellar medium. Cosmic magnetic fields. Cosmic rays. An introduction to physical cosmology.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 4 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

Integrated circuits, history and future trends. Solid state electronics, the MOS-transistor and CMOS. Integrated circuit fabrication, crystal growth, oxidation, doping, diffusion, ion implantation, lithography, deposition and etching of thin fi ms, microelectromechanical systems (MEMS).

The goal is to introduce the limits of single particle models of condensed matter and explore particle interactions. Curriculum: Electric- and magnetic susceptibility in insulating and semiconducting materials. Electron transport, the Boltzmann equation and the relaxation time approximation. Limits of single particle models. Interactions and many particle approximations. Exchange interaction and magnetic properties of condensed matter, Heisenberg model, spin waves. Superconductivity, the BCS model and the Ginzburg-Landau equation.

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

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.

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

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.

An introduction to astrobiology. Formation of the elements in the primordial plasma. Formation of heavy elements in stars and in their environments. Origin of galaxies, stellar systems, stars and planets. Formation of molecules and dust in the interstellar medium. Properties of Carbon and other elements necessary for life. Topics in biochemistry and thermodynamics. Origin and evolution of the Earth. Origin of water. The atmosphere. The Earth compared to other planets. What is life and what does it need? Origin and evolution of life on Earth. Life in extreme environments. Asteroids and impacts with the Earth. Effects of nearby supernovas. Is there life elsewhere in the Solar System, e.g. on Mars, Europa or Titan? Habitable worlds in the Universe. Extrasolar planets. The search for extraterrestrial intelligence. The Fermi paradox. Anthropic reasoning.

Nanostructures and Nanomaterials, Nanoparticles, Nanowires, Thin films, thin film growth, growth modes, transport properties.  Characterization of nanomaterials, Crystallography,Particle Size Determination, Surface Structure, Scanning Tunneling Microscope, Atomic Force Microscope, X-ray diffraction (XRD), X-ray reflectometry (XRR), Scanning Electron Microscpe (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructred Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

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

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Elements of set theory: Sets. Mappings. Relations, equivalence relations, orderings. Finite, infinite, countable and uncountable sets. Equipotent sets. Construction of the number systems. Metric spaces: Open sets and closed sets, convergent sequences and Cauchy sequences, cluster points of sets and limit points of sequences. Continuous mappings, convergence, uniform continuity. Complete metric spaces. Uniform convergence and interchange of limits. The Banach fixed point theorem; existence theorem about solutions of first-order differential equations. Completion of metric spaces. Compact metric spaces. Connected sets. Infinite series, in particular function series.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

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.

The Java programming language will be used to introduce basic practices in computer programming. Practice in programming is scheduled throughout the semester. An emphasis is placed on logical methods for writing program and good documentation. Main ideas related to computers and programming. Classes, objects and methods. Control statements. Strings and arrays, operations and built-in functons. Input and output. Inheritance. Ideas relatied to system design and good practices for program writing. Iteration and recursion. Searching and Sorting.

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.

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.

Basics of linear algebra over the reals with emphasis on the theoretical side. 

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 nullspace. 
The dot product, length and angle measures.  Volumes in higher dimensions 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.

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.

Introduction to the theory of Special Relativity and some basic concepts of General Relativity.

The need for Special Relativity (light propagation and key historical experiments). Einstein's principle of relativity, time dilation and length contraction. The geometry of spacetime (Minkowski space), the Lorentz transformation and causality. Kinematics, dynamics and electromagnetism in Special Relativity.
A brief introduction to General Relativity.

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.

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.

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.

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.

Python tools related to data analysis and plotting. Mathematical concepts such as vectors, matrices, differential operators in three dimensions, coordinate transformations, partial differential equations and Fourier series and their relation to undergraduate courses in physics and engineering. We will emphasize applications and problem solving.

This is an extension of the course "Probability and Statistics" STÆ203G. The basic concepts of probability are considered in more detail with emphasis on definitions and proofs. The course is a preparation for the two M-courses in probability and the two M-courses in statistics that are taught alternately every other year.

Topics beyond those discussed in the probability part of STÆ203G:

Kolmogorov's definition. Proofs of propositions on compound events and conditional probability. Proofs for discrete and continuous variables of propositions on expectation, variance, covariance, correlation, and conditional expectation and variance. Proofs of propositions for Bernoulli, binomial, Poisson, geometric, uniform, exponential, and gamma variables. Proof of the tail-summing proposition for expectation and the application to the geometric variable. Proof of the proposition on memoryless and exponential variables. Derivation of the distribution of sums of independent variables such as binomial, Poisson, normal, and gamma variables. Probability and moment generating functions.

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.

The course is an introduction to three important tools of applied mathematics, namely ordinary differential equations, Fourier-series and partial differential equations.  Some basic theoretical properties are proved and solution methods presented. 

Subject matter: Ordinary differential equations: linear differential equations of order n, the Cauchy problem, Picard's existence theorem, solution by power series and equations with singular points.  Fourier series: convergence point-wise, uniformly and in the mean-square, Parseval's equation.  Partial differential equations:

the heat equation and the wave equation solved on a finite interval by separation of variables and Fourier series and their solutions compared, the Dirichlet problem for the Laplace equation on the rectangle and the disc, the Poisson integral formula.

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.

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.

The course is devoted to theoretical foundations of wave and quantum mechanics. The main concepts characterizing classical waves, such as wave equation, plane waves, wavepackets and phase and group velocity are discussed and then, after the introduction of the concept of particle-wave dualism are used to describe the properties of the de Broglie material waves corresponding to quantum particles. Dynamic and stationary Schrodinger equations are introduced, and their solutions for a set of physically important particular cases, including quantum tunneling, quantum potential well, quantum harmonic oscillator and Coulomb potential are analyzed in all necessary detail. The last part of the course is devoted to the quantum description of spin.

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.

Python tools related to data analysis and manipulation of graphs. Differential equations and their use in the description of physical systems. Partial differential equations and boundary value problems. Special functions and their relation to important problems in physics. We will emphasize applications and problem solving.

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.

Introduction to atomic and molecular physics and modern optics. Electronic structure of atoms, the periodic table, chemical bonds and molecules, rotational and vibrational states, interaction between light and matter, symmetry and selection rules, polarisation, resonators and interferometers, atomic and molecular spectroscopy, optical amplification, lasers. The course includes three laboratory exercises.

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.

The course is devoted to the foundations of nuclear and elementary particle physics. It consists of the lectures on the corresponding theory and a laboratory of 2 week duration. In theoretical part students learn about basic ideas of nuclear physics, such as simplest nuclear models, basics of the scattering physics, types of elementary particles and their fundamental interactions. After that basics of the relativistic wave equations are introduced. The cases of Klein-Gordon, Higgs, and Dirac equations are considered. Higgs equation is used to introduce the fundamental concept of spontaneous symmetry breaking, necessary for the understanding of the appearance of a Higgs boson.  Solution of the Dirac equation for free particles is analyzed, and related fundamental concepts of antiparticles, helicity and chirality are considered in detail. 

The postulates and formalism of quantum mechanics. One-dimensional systems. Angular momentum, spin, two level systems. Particles in a central potential, the hydrogen atom. Approximation methods. Time independent and time dependent perturbation. Scattering.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Presentation of important techniques used in experimental physics and of various phenomena related to the subject matter of the second and third year of the Physics curriculum. Six extensive experiments are made, most of which are related to active research in experimental physics at the Science Institute of the University of Iceland.  The course emphasizes independence in carrying out the experiments, data analysis and literature search.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 8 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Seminar course on topics of current interest in astrophysics and cosmology.

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

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.

Selected topics in theoretical and experimental physics. Each student gives one lecture on a topic of his or her choice.

Introduction to how numerical analysis is used to explore the properties of physical system. Programming environment and graphical representation.  The application of functional bases to solve simple models in quantum and statistical physics. Parallel processing on clusters.  Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing

Identical particles, second quantization. Density operators, pure and mixed quantum states. Symmetries in quantum mechanics, the rotation group, addition of angular momenta, tensor operators, Wigner-Eckardt theorem. Interaction of atoms and radiation, spontaneous emission. Feynman path integrals.

The basis of the atomic theory. Stoichiometry. Types of chemical reactions and solution stoichiometry. Properties of gases. Chemical equilibrium. Acids and bases. Applications of aqueous equilibria. Chemical thermodynamics. Enthropy, free energy and equilibrium. Electrochemistry. Chemical kinetics. Physical properties of solutions.

An introduction to the physics of the Earth. The course should be suitable as a first course for those majoring in geophysics and for geology students wanting to become familiar with the subject. Gravity, shape and rotation of the Earth, gravity anomalies. The geomagnetic field, magnetic anomalies, palaeomagnetism. Earthquakes and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Origin and age of the Earth. Dating with radioactive elements. Geophysics of Iceland, introduction to geophysical research in Iceland.

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

Taught if sufficient number of students. May be taugth 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.

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.

This course is only for exchange students. It is taught with JEÐ301G tektonik. The subject of the course is active tectonic movements with emphasis on processes currently active in Iceland. Theory of plate tectonics, plate velocity models, both relative and absolute. Elastic and ductile behaviour of rocks in the crust and mantle. Brittle fracturing. Plate boundary deformation. Rifts and rifting structures. Transcurrent faulting and associated structures. Earthquakes and faulting. Measuring crustal movements, GPS-geodesy, levelling, SAR-interferometry, tilt- and strainmeters. A one-day field project will be carried out in an active area. Additionally, one day field trip to the plate boundary areas of SW-Iceland. Five home exercises are assigned. Solutions and report are to be handed in. A 3-hour written exam will be held at the end of the semester. Reports of exercises and field project are obligatory and count 20% towards a grade.

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.

Complex numbers and the topology of the complex plane. Sequences and series of complex numbers. Differentiable and holomorphic functions. Sequences and series of functions; power series. Path integration and primitives. The exponential function and related functions. Winding numbers. The Cauchy theorem, the integral formula of Cauchy and consequences. The identity theorem, the open mapping theorem and the maximum principle. Laurent series, isolated singularities and their classification. The theorem of residues and residue calculus. The argument principle and Rouché's theorem. Connections with real analysis: The Cauchy-Riemann equations, harmonic functions and the integral formulas of Poisson and Schwarz. Holomorphic functions defined by integrals (e. g. the Laplace transformation). Conformal mapping and the Riemann mapping theorem.

The object of the course is to give a firm and rigorous foundation for more advanced studies in partial differential equations. Contents: first order equations; the Cauchy-Kowalevski theorem; techniques of analysis (Lebesgue-integral, convolutions, Fourier-transform); distributions; fundamental solutions; the Laplace operator; the heat operator.  The course is mainly intended for postgraduate students with a good background in analysis.

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.

An introduction to astrophysical problems with emphasis on underlying physical principles. -- The nature of stars. Equations of state, stellar energy generation, radiative transfer. Stellar structure and evolution. Gravitational collapse and supernova explosions. Physics of white dwarfs, neutron stars and black holes. Compact binary systems. X-ray sources. Pulsars. Galaxies, their structure, formation and evolution. Active galaxies. The interstellar medium. Cosmic magnetic fields. Cosmic rays. An introduction to physical cosmology.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 4 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

Integrated circuits, history and future trends. Solid state electronics, the MOS-transistor and CMOS. Integrated circuit fabrication, crystal growth, oxidation, doping, diffusion, ion implantation, lithography, deposition and etching of thin fi ms, microelectromechanical systems (MEMS).

The goal is to introduce the limits of single particle models of condensed matter and explore particle interactions. Curriculum: Electric- and magnetic susceptibility in insulating and semiconducting materials. Electron transport, the Boltzmann equation and the relaxation time approximation. Limits of single particle models. Interactions and many particle approximations. Exchange interaction and magnetic properties of condensed matter, Heisenberg model, spin waves. Superconductivity, the BCS model and the Ginzburg-Landau equation.

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

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.

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

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.

An introduction to astrobiology. Formation of the elements in the primordial plasma. Formation of heavy elements in stars and in their environments. Origin of galaxies, stellar systems, stars and planets. Formation of molecules and dust in the interstellar medium. Properties of Carbon and other elements necessary for life. Topics in biochemistry and thermodynamics. Origin and evolution of the Earth. Origin of water. The atmosphere. The Earth compared to other planets. What is life and what does it need? Origin and evolution of life on Earth. Life in extreme environments. Asteroids and impacts with the Earth. Effects of nearby supernovas. Is there life elsewhere in the Solar System, e.g. on Mars, Europa or Titan? Habitable worlds in the Universe. Extrasolar planets. The search for extraterrestrial intelligence. The Fermi paradox. Anthropic reasoning.

Nanostructures and Nanomaterials, Nanoparticles, Nanowires, Thin films, thin film growth, growth modes, transport properties.  Characterization of nanomaterials, Crystallography,Particle Size Determination, Surface Structure, Scanning Tunneling Microscope, Atomic Force Microscope, X-ray diffraction (XRD), X-ray reflectometry (XRR), Scanning Electron Microscpe (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructred Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

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

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Elements of set theory: Sets. Mappings. Relations, equivalence relations, orderings. Finite, infinite, countable and uncountable sets. Equipotent sets. Construction of the number systems. Metric spaces: Open sets and closed sets, convergent sequences and Cauchy sequences, cluster points of sets and limit points of sequences. Continuous mappings, convergence, uniform continuity. Complete metric spaces. Uniform convergence and interchange of limits. The Banach fixed point theorem; existence theorem about solutions of first-order differential equations. Completion of metric spaces. Compact metric spaces. Connected sets. Infinite series, in particular function series.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

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.

The Java programming language will be used to introduce basic practices in computer programming. Practice in programming is scheduled throughout the semester. An emphasis is placed on logical methods for writing program and good documentation. Main ideas related to computers and programming. Classes, objects and methods. Control statements. Strings and arrays, operations and built-in functons. Input and output. Inheritance. Ideas relatied to system design and good practices for program writing. Iteration and recursion. Searching and Sorting.

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.

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.

Basics of linear algebra over the reals with emphasis on the theoretical side. 

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 nullspace. 
The dot product, length and angle measures.  Volumes in higher dimensions 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.

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.

Introduction to the theory of Special Relativity and some basic concepts of General Relativity.

The need for Special Relativity (light propagation and key historical experiments). Einstein's principle of relativity, time dilation and length contraction. The geometry of spacetime (Minkowski space), the Lorentz transformation and causality. Kinematics, dynamics and electromagnetism in Special Relativity.
A brief introduction to General Relativity.

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.

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.

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.

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.

Python tools related to data analysis and plotting. Mathematical concepts such as vectors, matrices, differential operators in three dimensions, coordinate transformations, partial differential equations and Fourier series and their relation to undergraduate courses in physics and engineering. We will emphasize applications and problem solving.

This is an extension of the course "Probability and Statistics" STÆ203G. The basic concepts of probability are considered in more detail with emphasis on definitions and proofs. The course is a preparation for the two M-courses in probability and the two M-courses in statistics that are taught alternately every other year.

Topics beyond those discussed in the probability part of STÆ203G:

Kolmogorov's definition. Proofs of propositions on compound events and conditional probability. Proofs for discrete and continuous variables of propositions on expectation, variance, covariance, correlation, and conditional expectation and variance. Proofs of propositions for Bernoulli, binomial, Poisson, geometric, uniform, exponential, and gamma variables. Proof of the tail-summing proposition for expectation and the application to the geometric variable. Proof of the proposition on memoryless and exponential variables. Derivation of the distribution of sums of independent variables such as binomial, Poisson, normal, and gamma variables. Probability and moment generating functions.

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.

The course is an introduction to three important tools of applied mathematics, namely ordinary differential equations, Fourier-series and partial differential equations.  Some basic theoretical properties are proved and solution methods presented. 

Subject matter: Ordinary differential equations: linear differential equations of order n, the Cauchy problem, Picard's existence theorem, solution by power series and equations with singular points.  Fourier series: convergence point-wise, uniformly and in the mean-square, Parseval's equation.  Partial differential equations:

the heat equation and the wave equation solved on a finite interval by separation of variables and Fourier series and their solutions compared, the Dirichlet problem for the Laplace equation on the rectangle and the disc, the Poisson integral formula.

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.

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.

The course is devoted to theoretical foundations of wave and quantum mechanics. The main concepts characterizing classical waves, such as wave equation, plane waves, wavepackets and phase and group velocity are discussed and then, after the introduction of the concept of particle-wave dualism are used to describe the properties of the de Broglie material waves corresponding to quantum particles. Dynamic and stationary Schrodinger equations are introduced, and their solutions for a set of physically important particular cases, including quantum tunneling, quantum potential well, quantum harmonic oscillator and Coulomb potential are analyzed in all necessary detail. The last part of the course is devoted to the quantum description of spin.

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.

Python tools related to data analysis and manipulation of graphs. Differential equations and their use in the description of physical systems. Partial differential equations and boundary value problems. Special functions and their relation to important problems in physics. We will emphasize applications and problem solving.

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.

Introduction to atomic and molecular physics and modern optics. Electronic structure of atoms, the periodic table, chemical bonds and molecules, rotational and vibrational states, interaction between light and matter, symmetry and selection rules, polarisation, resonators and interferometers, atomic and molecular spectroscopy, optical amplification, lasers. The course includes three laboratory exercises.

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.

The course is devoted to the foundations of nuclear and elementary particle physics. It consists of the lectures on the corresponding theory and a laboratory of 2 week duration. In theoretical part students learn about basic ideas of nuclear physics, such as simplest nuclear models, basics of the scattering physics, types of elementary particles and their fundamental interactions. After that basics of the relativistic wave equations are introduced. The cases of Klein-Gordon, Higgs, and Dirac equations are considered. Higgs equation is used to introduce the fundamental concept of spontaneous symmetry breaking, necessary for the understanding of the appearance of a Higgs boson.  Solution of the Dirac equation for free particles is analyzed, and related fundamental concepts of antiparticles, helicity and chirality are considered in detail. 

The postulates and formalism of quantum mechanics. One-dimensional systems. Angular momentum, spin, two level systems. Particles in a central potential, the hydrogen atom. Approximation methods. Time independent and time dependent perturbation. Scattering.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Presentation of important techniques used in experimental physics and of various phenomena related to the subject matter of the second and third year of the Physics curriculum. Six extensive experiments are made, most of which are related to active research in experimental physics at the Science Institute of the University of Iceland.  The course emphasizes independence in carrying out the experiments, data analysis and literature search.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 8 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Seminar course on topics of current interest in astrophysics and cosmology.

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

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.

Selected topics in theoretical and experimental physics. Each student gives one lecture on a topic of his or her choice.

Introduction to how numerical analysis is used to explore the properties of physical system. Programming environment and graphical representation.  The application of functional bases to solve simple models in quantum and statistical physics. Parallel processing on clusters.  Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing

Identical particles, second quantization. Density operators, pure and mixed quantum states. Symmetries in quantum mechanics, the rotation group, addition of angular momenta, tensor operators, Wigner-Eckardt theorem. Interaction of atoms and radiation, spontaneous emission. Feynman path integrals.

The basis of the atomic theory. Stoichiometry. Types of chemical reactions and solution stoichiometry. Properties of gases. Chemical equilibrium. Acids and bases. Applications of aqueous equilibria. Chemical thermodynamics. Enthropy, free energy and equilibrium. Electrochemistry. Chemical kinetics. Physical properties of solutions.

An introduction to the physics of the Earth. The course should be suitable as a first course for those majoring in geophysics and for geology students wanting to become familiar with the subject. Gravity, shape and rotation of the Earth, gravity anomalies. The geomagnetic field, magnetic anomalies, palaeomagnetism. Earthquakes and seismic waves. Layered structure of the Earth, heat transport and the internal heat of the Earth. Origin and age of the Earth. Dating with radioactive elements. Geophysics of Iceland, introduction to geophysical research in Iceland.

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

Taught if sufficient number of students. May be taugth 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.

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.

This course is only for exchange students. It is taught with JEÐ301G tektonik. The subject of the course is active tectonic movements with emphasis on processes currently active in Iceland. Theory of plate tectonics, plate velocity models, both relative and absolute. Elastic and ductile behaviour of rocks in the crust and mantle. Brittle fracturing. Plate boundary deformation. Rifts and rifting structures. Transcurrent faulting and associated structures. Earthquakes and faulting. Measuring crustal movements, GPS-geodesy, levelling, SAR-interferometry, tilt- and strainmeters. A one-day field project will be carried out in an active area. Additionally, one day field trip to the plate boundary areas of SW-Iceland. Five home exercises are assigned. Solutions and report are to be handed in. A 3-hour written exam will be held at the end of the semester. Reports of exercises and field project are obligatory and count 20% towards a grade.

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.

Complex numbers and the topology of the complex plane. Sequences and series of complex numbers. Differentiable and holomorphic functions. Sequences and series of functions; power series. Path integration and primitives. The exponential function and related functions. Winding numbers. The Cauchy theorem, the integral formula of Cauchy and consequences. The identity theorem, the open mapping theorem and the maximum principle. Laurent series, isolated singularities and their classification. The theorem of residues and residue calculus. The argument principle and Rouché's theorem. Connections with real analysis: The Cauchy-Riemann equations, harmonic functions and the integral formulas of Poisson and Schwarz. Holomorphic functions defined by integrals (e. g. the Laplace transformation). Conformal mapping and the Riemann mapping theorem.

The object of the course is to give a firm and rigorous foundation for more advanced studies in partial differential equations. Contents: first order equations; the Cauchy-Kowalevski theorem; techniques of analysis (Lebesgue-integral, convolutions, Fourier-transform); distributions; fundamental solutions; the Laplace operator; the heat operator.  The course is mainly intended for postgraduate students with a good background in analysis.

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.

An introduction to astrophysical problems with emphasis on underlying physical principles. -- The nature of stars. Equations of state, stellar energy generation, radiative transfer. Stellar structure and evolution. Gravitational collapse and supernova explosions. Physics of white dwarfs, neutron stars and black holes. Compact binary systems. X-ray sources. Pulsars. Galaxies, their structure, formation and evolution. Active galaxies. The interstellar medium. Cosmic magnetic fields. Cosmic rays. An introduction to physical cosmology.

The student consults a teacher and selects a subject in theoretical or experimental physics for a research project on which he works under the supervision of a member of the academic staff. The project takes about 4 weeks of work and is completed with a written report by the student. In general any of the teacher of the Physics Department can supervise a project of this kind.

Integrated circuits, history and future trends. Solid state electronics, the MOS-transistor and CMOS. Integrated circuit fabrication, crystal growth, oxidation, doping, diffusion, ion implantation, lithography, deposition and etching of thin fi ms, microelectromechanical systems (MEMS).

The goal is to introduce the limits of single particle models of condensed matter and explore particle interactions. Curriculum: Electric- and magnetic susceptibility in insulating and semiconducting materials. Electron transport, the Boltzmann equation and the relaxation time approximation. Limits of single particle models. Interactions and many particle approximations. Exchange interaction and magnetic properties of condensed matter, Heisenberg model, spin waves. Superconductivity, the BCS model and the Ginzburg-Landau equation.

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

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.

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

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.

An introduction to astrobiology. Formation of the elements in the primordial plasma. Formation of heavy elements in stars and in their environments. Origin of galaxies, stellar systems, stars and planets. Formation of molecules and dust in the interstellar medium. Properties of Carbon and other elements necessary for life. Topics in biochemistry and thermodynamics. Origin and evolution of the Earth. Origin of water. The atmosphere. The Earth compared to other planets. What is life and what does it need? Origin and evolution of life on Earth. Life in extreme environments. Asteroids and impacts with the Earth. Effects of nearby supernovas. Is there life elsewhere in the Solar System, e.g. on Mars, Europa or Titan? Habitable worlds in the Universe. Extrasolar planets. The search for extraterrestrial intelligence. The Fermi paradox. Anthropic reasoning.

Nanostructures and Nanomaterials, Nanoparticles, Nanowires, Thin films, thin film growth, growth modes, transport properties.  Characterization of nanomaterials, Crystallography,Particle Size Determination, Surface Structure, Scanning Tunneling Microscope, Atomic Force Microscope, X-ray diffraction (XRD), X-ray reflectometry (XRR), Scanning Electron Microscpe (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructred Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

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

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Elements of set theory: Sets. Mappings. Relations, equivalence relations, orderings. Finite, infinite, countable and uncountable sets. Equipotent sets. Construction of the number systems. Metric spaces: Open sets and closed sets, convergent sequences and Cauchy sequences, cluster points of sets and limit points of sequences. Continuous mappings, convergence, uniform continuity. Complete metric spaces. Uniform convergence and interchange of limits. The Banach fixed point theorem; existence theorem about solutions of first-order differential equations. Completion of metric spaces. Compact metric spaces. Connected sets. Infinite series, in particular function series.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

This course aims to introduce students to the nature and development of science by examining episodes of its history and by disucssing recent theories concerning the nature, aims, and development of science. A special emphasis will be placed on the history of physical science from Aristotle to Newton, including developments in astronomy during the scientific revolution of the 16th and 17th century. We will also specifically examine the history of Darwin’s theory of evolution by natural selection. These episodes and many others will be viewed through the lens of various theories of scientific progress, and through recent views about interactions between science and society at large. The course material may change depending on the students’ interest.

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.

The Java programming language will be used to introduce basic practices in computer programming. Practice in programming is scheduled throughout the semester. An emphasis is placed on logical methods for writing program and good documentation. Main ideas related to computers and programming. Classes, objects and methods. Control statements. Strings and arrays, operations and built-in functons. Input and output. Inheritance. Ideas relatied to system design and good practices for program writing. Iteration and recursion. Searching and Sorting.

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.

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.

Basics of linear algebra over the reals with emphasis on the theoretical side. 

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 nullspace. 
The dot product, length and angle measures.  Volumes in higher dimensions 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.

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.