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.

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.

Basics of linear algebra over the reals.  

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

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.

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 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.

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.

Order of magnitude estimates, scaling relations, and dimensional analysis. Plotting with matplotlib. Complex numbers, oscillations and Fourier-series. Mechanics and the time derivatives of vectors. Particle trajectories in polar coordinates. Derivatives, the chain rule and equations of state. Scalar and vector potentials and connection to electromagnetism. Stokes and divergence theorems and Maxwell's equations. We emphasize applications and problem solving.

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.

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 quantum mechanics. 

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

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.

Python tools related to general data and time series analysis. The method of least squares, linear and non-linear fitting. Fourier transforms, fast Fourier transforms (FFT), spectral analysis and convolution. Differential equations, including the Laplace equation 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.

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.

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.

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.

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.

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 Microscope (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructured Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

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

Minimum number of students registered for the course to be taught: 10

This course will cover basics in intellectual property rights with emphasis on patents. What is intellectual property and when and how can they best be protected? How does intellectual property rights work (e.g. patents), and how can they be used and applied in innovation and industry. The system‘s organization will be covered, as well as the patent process, making a financial plan relating to patents, and database searches.

x

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.

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.

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 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.

The objective of the course is that students get the skills to:

1.    Understand the main concepts in accounting, cost theory and investment theory.

2.    Be able to use methods of measuring the economic feasibility of technical projects.

3.    Be able to develop computer models to assess the profitability of investments, the value of companies and pricing of bonds

Among topics included are accounting, cost theory, cash flow analysis, investment theory, measures of profitability including net present value and internal rate of return, and the building of profitability models. The course ends with a group assignment where the students exercise the development of computer models for feasibility assessment of projects.

The course is an introductory course in project management. It introduces key concepts of project management and covers context and selection of projects, project planning, project monitoring, management of project teams, and project closure. Students create and execute project plans in groups. Special emphasis is on using of project management for managing technological innovation in organizations.

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 thorough treatment of the fundamentals of biochemistry - part one; structure and function of macromolecules. The scope of biochemistry. Water and its properties. Interactions in biomolecules. Amino acids, peptides and the structure of proteins. Protein function.  Protein stability, folding, and dynamics related to function. Carbohydrates and glycobiology. Lipids, membranes and membrane proteins. Enzyme kinetics, regulation of enzyme activity, and mechanisms of enzyme catalysis. Signal transduction and membrane receptors. Structure of nucleic acids, stability, and basic recombinant technology. Final grade is combined from the final exam (85% ) and a midterm exam (15%).

Lectures:
Twice weekly (2 x 40 min.) Probelm solving class (2 x 40 min.) weekly.

Course evaluation:
Final exam (3 hours): 85% of final grade.
Midterm: 15% of final grade.

Textbook:
Nelson D.L. & Cox M.M. Lehninger: Principles of Biochemistry, 8th Edition, 2021

Lectures: Mendelian inheritance. Sex chromosomes. Cytoplasmic inheritance. Chromosomes. Cell division (mitosis and meiosis). Life cycles. Linkage and recombination in eukaryotes. Bacterial genetics. Gene mapping and tetrad analysis. Genotype and phenotype. Chromosomal changes. DNA: Structure and replication. RNA: Transcription. Rgulation of gene transcription. Gene isolation and manipulation. Genomics. Transposons.  Mutations. Repair and recombination.  Model organisms. Laboratory work: : I. The fruitfly Drosophila melanogaster. II. Mitosis in onions. III. Plasmids and restriction enzymes. IV. PCR. V. Analysis of asci from Sordaria fimicola.

Exam: Laboratory and problems 25%, written 75%. Minimum mark needed for each part.

The cell biology part includes four lectures each week for 14 weeks (4L week for 14 weeks). The content includes: Introduction to cell biology, structure and evolution of eukaryotic cells. The main emphasis is on eukaryotic cells. Chemistry of the cell and energy conversion, structure and function of cellular macromolecules. The structure and function of cellular organs and functional units like the cell membrane, nucleus, mitochondria, chloroplasts, cytoskeleton, golgi-system, lysosomes and peroxisomes. Intracellular regulation and signal pathways linked to communication between cells, together with cell differentiation and cancer. Details on extracellular matrix are included and basic immunology.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

The aim of the course is:- To give students overview of processes in materials engineering;- To encourage students to think about feasible ways to utilize renewable energy. The course will cover the industrial processes in some of the larger Icelandic companies, including the production of ferro-alloys, aluminium smelting, rockwool production, recycling of steel, algea and diatomitemining, and production of sodium chlorine, fertilizers, cement. The course will also cover some of the larger material engineering processes that are not in practice in Iceland but may be a feasible option for Icelandic industry. Students will get good overview of the processes, required materials, source of power and power consumption, pollution, products etc. Discussions will be held on the financial background for individual processes, covering aspects such as production cost, profit and the influences of market share changes. Grades are based on 2 larger projects the students work on through the semester. Field trips are an important part of the course.

The objective of the course is to teach the fundamental principles of materials science so the student can better understand material behavior and select appropriate materials for a given application. Theoretical basis is given for the understanding of material behaviour from a microscopic view. The course includes the following topics: crystalline structures, imperfections, diffusion, mechanical properties, deformation and strengthening mechanisms, fracture and fatique, phase diagrams, phase transformations, thermal processing of metal alloys, types of materials (metal alloys, polymers, ceramics, composites), corrosion and degradation of of materials. The course includes homework problems and practical classes in laboratory.

Basic thermodynamic and electrochemical principles that cause corrosion. Procedures of electrochemical measurements used to investigate corrosion behavior. Methods of corrosion protection and prevention, materials selection and design.

The course is taught every other year on even numbered years.

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.

Objective:
To participate in the international Formula Student project by designing and building an electric race car with the purpose of participating in international competitions amongst universities. Strict requirements must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part A is the project preparation, planning and technical design.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

x

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).

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.

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.

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.

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.

Introduction to processes and material and energy balance calculations applied to industrial processes. Analysis of gas behavior, gas-liquid systems, and phase equilibrium. Material balances, including reaction systems and multiple-unit systems. Energy balances, including reaction systems and multiple-unit systems, and combined energy-material balances.

A systematic introduction to the use of process simulators (like Aspen) to model, design and optimize chemical manufacturing processes. The selection, optimization and combination of reactors, separation equipment and heat exchangers. An introduction to the concepts and principles of project economics.

This course provides an introduction to the design and analysis of chemical reactors, including batch, plug flow, continuous stirred tank reactors, and bioreactors. It covers key concepts in chemical thermodynamics, reaction kinetics, and catalysis, enabling students to develop a strong foundational knowledge in chemical reaction engineering. The course also includes guest lectures from industry experts and student presentations, fostering a connection to real-world applications.

In this course, the main metabolic processes of cells are studied, with a focus on carbohydrate, fat, and protein metabolism, as well as the metabolic regulation of these processes. The course begins with a detailed examination of carbohydrate metabolism, including glycolysis (both aerobic and anaerobic), the citric acid cycle, and the pentose phosphate pathway. Then we continue into pathways such as gluconeogenesis, glycogen breakdown, and then into how carbohydrate metabolism is regulated.

Next, the focus shifts to fat metabolism, where the breakdown of triglycerides, fatty acid oxidation, and fatty acid synthesis are explained. Special emphasis is placed on the regulation of fat metabolism and the control of enzymes involved in these processes. Following this, protein metabolism is addressed, where protein hydrolysis, amino acid degradation, and the urea cycle are studied.

The course also covers the integration and regulation of metabolic pathways, with a focus on the complex regulation that occurs in the key steps of these pathways, considering both intracellular signals and hormones. It examines how these processes adapt to various conditions to maintain homeostasis and the effects of disruptions in their regulation. Lastly, photosynthesis and the Calvin cycle are covered.

This course is highly beneficial for those seeking an in-depth understanding of biochemical processes and the biochemistry of the human body.

Lectures are held twice a week (2 x 40 minutes) over 13-14 weeks. 

During this course, students will be introduced to organisms and acellular entities too small to be seen by the unaided eye.  They can acquire knowledge on the characteristics of bacteria, archaea, viruses and eukaryotic microorganisms.  The course will explain the importance of microorganisms, how they live in diverse and dynamic ecosystems and how some affect humans, for example by being valuable for the food industry or by causing disease.  The students will gain laboratory experience and practice aseptic techniques. 

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.

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

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Systems biology is an interdisciplinary field that studies the biological phenomena that emerge from multiple interacting biological elements. Understanding how biological systems change across time is a particular focus of systems biology. In this course, we will prioritize aspects of systems biology relevant to human health and disease.

This course provides an introduction to 1) basic principles in modelling molecular networks, both gene regulatory and metabolic networks; 2) cellular phenomena that support homeostasis like tissue morphogenesis and microbiome resilience, and 3) analysis of molecular patterns found in genomics data at population scale relevant to human disease such as patient classification and biomarker discovery. In this manner, the course covers the three major scales in systems biology: molecules, cells and organisms.

The course activities include reading and interpreting scientific papers, implementation of computational algorithms, working on a research project and presentation of scientific results.

Lectures will comprise of both (1) presentations on foundational concepts and (2) hands-on sessions using Python as the programming language. The course will be taught in English.

Mechanical systems and mechatronics system elements. Mechanism, motors, drives, motion converters, sensors and transducers. Signal processing and microprocessor.

In this course students are introduced to the basic concepts and methods for parametric representation of curves such as the Bezier-, Hermite- and NURBS curves.  Students will learn about the methods for representing three-dimensional wireframe-, solid- and surface models.  The course will cover the use of parameters when developing and creating three-dimensional modeling, the creation of assembly drawings using mating operators and how different engineering software solutions can communicate. 

The course provides a good fundamental overview of the available engineering software solutions – their advantages and limitations – and the students will learn about the current trends in their field, e.g. in the analysis, simulation, prototyping and manufacturing.  The current trends will be indroduced through guest lectures, company visits and a mini-seminar where the students write articles and present new and exciting research or new techniques (based on peer-review papers). 

Concurrently with the lectures, students work on an unstructured engineering project where they will engineer and build a working prototype, write the results in a report and present the results.

Goal: Enable the students to: 1: Study thermodynamics from the viewpoint of the second law of thermodynamics 2. Understand standard power cycles, and their use for analysis of power plants 3. Understand air conditioning systems and their necessity 4. Understand thermochemistry and be able to estimate heat release through combustion. Content: Work, heat and energy conversion. Exergy and anergy. Energy, energy price and energy quality. Standard power and refrigeration cycles. Steam power cycles, geothermal utilization. Gas mixtures, moist air, ventilation and air purifiers. The Mollier i-x chart. Thermochemistry, combustion and reactions, chemical equilibrium. New energy systems. Exercises, design project.

Heat conduction, one and two dimensional systems, steady and unsteady heat conduction, numerical analysis of heat conduction systems. Fins and enlarged heat transfer surfaces. Heat transfer by convection, laminar and turbulent flow. Free and forced convection. Evaporation and condensation. Thermal radiation, Stefan-Boltzmann's and Planck's laws. Thermal radiation properties of materials. Shape factors, radiative heat exchange between surfaces, radiation properties of gases. Heat exchangers and their design. Special topics in heat transfer.

To participate in the international Formula Student project by designing and bulding an electric race car with the purpose of participating in international competitions amongst universities. Strict requirement must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part B is the construction of the car and preparing of participation in the international student competition.

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. 

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.

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.

Basics of linear algebra over the reals.  

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

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.

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 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.

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.

Order of magnitude estimates, scaling relations, and dimensional analysis. Plotting with matplotlib. Complex numbers, oscillations and Fourier-series. Mechanics and the time derivatives of vectors. Particle trajectories in polar coordinates. Derivatives, the chain rule and equations of state. Scalar and vector potentials and connection to electromagnetism. Stokes and divergence theorems and Maxwell's equations. We emphasize applications and problem solving.

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.

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 quantum mechanics. 

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

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.

Python tools related to general data and time series analysis. The method of least squares, linear and non-linear fitting. Fourier transforms, fast Fourier transforms (FFT), spectral analysis and convolution. Differential equations, including the Laplace equation 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.

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.

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.

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.

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.

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 Microscope (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructured Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

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

Minimum number of students registered for the course to be taught: 10

This course will cover basics in intellectual property rights with emphasis on patents. What is intellectual property and when and how can they best be protected? How does intellectual property rights work (e.g. patents), and how can they be used and applied in innovation and industry. The system‘s organization will be covered, as well as the patent process, making a financial plan relating to patents, and database searches.

x

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.

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.

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 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.

The objective of the course is that students get the skills to:

1.    Understand the main concepts in accounting, cost theory and investment theory.

2.    Be able to use methods of measuring the economic feasibility of technical projects.

3.    Be able to develop computer models to assess the profitability of investments, the value of companies and pricing of bonds

Among topics included are accounting, cost theory, cash flow analysis, investment theory, measures of profitability including net present value and internal rate of return, and the building of profitability models. The course ends with a group assignment where the students exercise the development of computer models for feasibility assessment of projects.

The course is an introductory course in project management. It introduces key concepts of project management and covers context and selection of projects, project planning, project monitoring, management of project teams, and project closure. Students create and execute project plans in groups. Special emphasis is on using of project management for managing technological innovation in organizations.

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 thorough treatment of the fundamentals of biochemistry - part one; structure and function of macromolecules. The scope of biochemistry. Water and its properties. Interactions in biomolecules. Amino acids, peptides and the structure of proteins. Protein function.  Protein stability, folding, and dynamics related to function. Carbohydrates and glycobiology. Lipids, membranes and membrane proteins. Enzyme kinetics, regulation of enzyme activity, and mechanisms of enzyme catalysis. Signal transduction and membrane receptors. Structure of nucleic acids, stability, and basic recombinant technology. Final grade is combined from the final exam (85% ) and a midterm exam (15%).

Lectures:
Twice weekly (2 x 40 min.) Probelm solving class (2 x 40 min.) weekly.

Course evaluation:
Final exam (3 hours): 85% of final grade.
Midterm: 15% of final grade.

Textbook:
Nelson D.L. & Cox M.M. Lehninger: Principles of Biochemistry, 8th Edition, 2021

Lectures: Mendelian inheritance. Sex chromosomes. Cytoplasmic inheritance. Chromosomes. Cell division (mitosis and meiosis). Life cycles. Linkage and recombination in eukaryotes. Bacterial genetics. Gene mapping and tetrad analysis. Genotype and phenotype. Chromosomal changes. DNA: Structure and replication. RNA: Transcription. Rgulation of gene transcription. Gene isolation and manipulation. Genomics. Transposons.  Mutations. Repair and recombination.  Model organisms. Laboratory work: : I. The fruitfly Drosophila melanogaster. II. Mitosis in onions. III. Plasmids and restriction enzymes. IV. PCR. V. Analysis of asci from Sordaria fimicola.

Exam: Laboratory and problems 25%, written 75%. Minimum mark needed for each part.

The cell biology part includes four lectures each week for 14 weeks (4L week for 14 weeks). The content includes: Introduction to cell biology, structure and evolution of eukaryotic cells. The main emphasis is on eukaryotic cells. Chemistry of the cell and energy conversion, structure and function of cellular macromolecules. The structure and function of cellular organs and functional units like the cell membrane, nucleus, mitochondria, chloroplasts, cytoskeleton, golgi-system, lysosomes and peroxisomes. Intracellular regulation and signal pathways linked to communication between cells, together with cell differentiation and cancer. Details on extracellular matrix are included and basic immunology.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

The aim of the course is:- To give students overview of processes in materials engineering;- To encourage students to think about feasible ways to utilize renewable energy. The course will cover the industrial processes in some of the larger Icelandic companies, including the production of ferro-alloys, aluminium smelting, rockwool production, recycling of steel, algea and diatomitemining, and production of sodium chlorine, fertilizers, cement. The course will also cover some of the larger material engineering processes that are not in practice in Iceland but may be a feasible option for Icelandic industry. Students will get good overview of the processes, required materials, source of power and power consumption, pollution, products etc. Discussions will be held on the financial background for individual processes, covering aspects such as production cost, profit and the influences of market share changes. Grades are based on 2 larger projects the students work on through the semester. Field trips are an important part of the course.

The objective of the course is to teach the fundamental principles of materials science so the student can better understand material behavior and select appropriate materials for a given application. Theoretical basis is given for the understanding of material behaviour from a microscopic view. The course includes the following topics: crystalline structures, imperfections, diffusion, mechanical properties, deformation and strengthening mechanisms, fracture and fatique, phase diagrams, phase transformations, thermal processing of metal alloys, types of materials (metal alloys, polymers, ceramics, composites), corrosion and degradation of of materials. The course includes homework problems and practical classes in laboratory.

Basic thermodynamic and electrochemical principles that cause corrosion. Procedures of electrochemical measurements used to investigate corrosion behavior. Methods of corrosion protection and prevention, materials selection and design.

The course is taught every other year on even numbered years.

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.

Objective:
To participate in the international Formula Student project by designing and building an electric race car with the purpose of participating in international competitions amongst universities. Strict requirements must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part A is the project preparation, planning and technical design.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

x

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).

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.

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.

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.

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.

Introduction to processes and material and energy balance calculations applied to industrial processes. Analysis of gas behavior, gas-liquid systems, and phase equilibrium. Material balances, including reaction systems and multiple-unit systems. Energy balances, including reaction systems and multiple-unit systems, and combined energy-material balances.

A systematic introduction to the use of process simulators (like Aspen) to model, design and optimize chemical manufacturing processes. The selection, optimization and combination of reactors, separation equipment and heat exchangers. An introduction to the concepts and principles of project economics.

This course provides an introduction to the design and analysis of chemical reactors, including batch, plug flow, continuous stirred tank reactors, and bioreactors. It covers key concepts in chemical thermodynamics, reaction kinetics, and catalysis, enabling students to develop a strong foundational knowledge in chemical reaction engineering. The course also includes guest lectures from industry experts and student presentations, fostering a connection to real-world applications.

In this course, the main metabolic processes of cells are studied, with a focus on carbohydrate, fat, and protein metabolism, as well as the metabolic regulation of these processes. The course begins with a detailed examination of carbohydrate metabolism, including glycolysis (both aerobic and anaerobic), the citric acid cycle, and the pentose phosphate pathway. Then we continue into pathways such as gluconeogenesis, glycogen breakdown, and then into how carbohydrate metabolism is regulated.

Next, the focus shifts to fat metabolism, where the breakdown of triglycerides, fatty acid oxidation, and fatty acid synthesis are explained. Special emphasis is placed on the regulation of fat metabolism and the control of enzymes involved in these processes. Following this, protein metabolism is addressed, where protein hydrolysis, amino acid degradation, and the urea cycle are studied.

The course also covers the integration and regulation of metabolic pathways, with a focus on the complex regulation that occurs in the key steps of these pathways, considering both intracellular signals and hormones. It examines how these processes adapt to various conditions to maintain homeostasis and the effects of disruptions in their regulation. Lastly, photosynthesis and the Calvin cycle are covered.

This course is highly beneficial for those seeking an in-depth understanding of biochemical processes and the biochemistry of the human body.

Lectures are held twice a week (2 x 40 minutes) over 13-14 weeks. 

During this course, students will be introduced to organisms and acellular entities too small to be seen by the unaided eye.  They can acquire knowledge on the characteristics of bacteria, archaea, viruses and eukaryotic microorganisms.  The course will explain the importance of microorganisms, how they live in diverse and dynamic ecosystems and how some affect humans, for example by being valuable for the food industry or by causing disease.  The students will gain laboratory experience and practice aseptic techniques. 

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.

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

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Systems biology is an interdisciplinary field that studies the biological phenomena that emerge from multiple interacting biological elements. Understanding how biological systems change across time is a particular focus of systems biology. In this course, we will prioritize aspects of systems biology relevant to human health and disease.

This course provides an introduction to 1) basic principles in modelling molecular networks, both gene regulatory and metabolic networks; 2) cellular phenomena that support homeostasis like tissue morphogenesis and microbiome resilience, and 3) analysis of molecular patterns found in genomics data at population scale relevant to human disease such as patient classification and biomarker discovery. In this manner, the course covers the three major scales in systems biology: molecules, cells and organisms.

The course activities include reading and interpreting scientific papers, implementation of computational algorithms, working on a research project and presentation of scientific results.

Lectures will comprise of both (1) presentations on foundational concepts and (2) hands-on sessions using Python as the programming language. The course will be taught in English.

Mechanical systems and mechatronics system elements. Mechanism, motors, drives, motion converters, sensors and transducers. Signal processing and microprocessor.

In this course students are introduced to the basic concepts and methods for parametric representation of curves such as the Bezier-, Hermite- and NURBS curves.  Students will learn about the methods for representing three-dimensional wireframe-, solid- and surface models.  The course will cover the use of parameters when developing and creating three-dimensional modeling, the creation of assembly drawings using mating operators and how different engineering software solutions can communicate. 

The course provides a good fundamental overview of the available engineering software solutions – their advantages and limitations – and the students will learn about the current trends in their field, e.g. in the analysis, simulation, prototyping and manufacturing.  The current trends will be indroduced through guest lectures, company visits and a mini-seminar where the students write articles and present new and exciting research or new techniques (based on peer-review papers). 

Concurrently with the lectures, students work on an unstructured engineering project where they will engineer and build a working prototype, write the results in a report and present the results.

Goal: Enable the students to: 1: Study thermodynamics from the viewpoint of the second law of thermodynamics 2. Understand standard power cycles, and their use for analysis of power plants 3. Understand air conditioning systems and their necessity 4. Understand thermochemistry and be able to estimate heat release through combustion. Content: Work, heat and energy conversion. Exergy and anergy. Energy, energy price and energy quality. Standard power and refrigeration cycles. Steam power cycles, geothermal utilization. Gas mixtures, moist air, ventilation and air purifiers. The Mollier i-x chart. Thermochemistry, combustion and reactions, chemical equilibrium. New energy systems. Exercises, design project.

Heat conduction, one and two dimensional systems, steady and unsteady heat conduction, numerical analysis of heat conduction systems. Fins and enlarged heat transfer surfaces. Heat transfer by convection, laminar and turbulent flow. Free and forced convection. Evaporation and condensation. Thermal radiation, Stefan-Boltzmann's and Planck's laws. Thermal radiation properties of materials. Shape factors, radiative heat exchange between surfaces, radiation properties of gases. Heat exchangers and their design. Special topics in heat transfer.

To participate in the international Formula Student project by designing and bulding an electric race car with the purpose of participating in international competitions amongst universities. Strict requirement must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part B is the construction of the car and preparing of participation in the international student competition.

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. 

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.

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.

Basics of linear algebra over the reals.  

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

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.

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 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.

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.

Order of magnitude estimates, scaling relations, and dimensional analysis. Plotting with matplotlib. Complex numbers, oscillations and Fourier-series. Mechanics and the time derivatives of vectors. Particle trajectories in polar coordinates. Derivatives, the chain rule and equations of state. Scalar and vector potentials and connection to electromagnetism. Stokes and divergence theorems and Maxwell's equations. We emphasize applications and problem solving.

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.

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 quantum mechanics. 

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

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.

Python tools related to general data and time series analysis. The method of least squares, linear and non-linear fitting. Fourier transforms, fast Fourier transforms (FFT), spectral analysis and convolution. Differential equations, including the Laplace equation 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.

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.

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.

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.

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.

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 Microscope (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructured Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

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

Minimum number of students registered for the course to be taught: 10

This course will cover basics in intellectual property rights with emphasis on patents. What is intellectual property and when and how can they best be protected? How does intellectual property rights work (e.g. patents), and how can they be used and applied in innovation and industry. The system‘s organization will be covered, as well as the patent process, making a financial plan relating to patents, and database searches.

x

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.

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.

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 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.

The objective of the course is that students get the skills to:

1.    Understand the main concepts in accounting, cost theory and investment theory.

2.    Be able to use methods of measuring the economic feasibility of technical projects.

3.    Be able to develop computer models to assess the profitability of investments, the value of companies and pricing of bonds

Among topics included are accounting, cost theory, cash flow analysis, investment theory, measures of profitability including net present value and internal rate of return, and the building of profitability models. The course ends with a group assignment where the students exercise the development of computer models for feasibility assessment of projects.

The course is an introductory course in project management. It introduces key concepts of project management and covers context and selection of projects, project planning, project monitoring, management of project teams, and project closure. Students create and execute project plans in groups. Special emphasis is on using of project management for managing technological innovation in organizations.

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 thorough treatment of the fundamentals of biochemistry - part one; structure and function of macromolecules. The scope of biochemistry. Water and its properties. Interactions in biomolecules. Amino acids, peptides and the structure of proteins. Protein function.  Protein stability, folding, and dynamics related to function. Carbohydrates and glycobiology. Lipids, membranes and membrane proteins. Enzyme kinetics, regulation of enzyme activity, and mechanisms of enzyme catalysis. Signal transduction and membrane receptors. Structure of nucleic acids, stability, and basic recombinant technology. Final grade is combined from the final exam (85% ) and a midterm exam (15%).

Lectures:
Twice weekly (2 x 40 min.) Probelm solving class (2 x 40 min.) weekly.

Course evaluation:
Final exam (3 hours): 85% of final grade.
Midterm: 15% of final grade.

Textbook:
Nelson D.L. & Cox M.M. Lehninger: Principles of Biochemistry, 8th Edition, 2021

Lectures: Mendelian inheritance. Sex chromosomes. Cytoplasmic inheritance. Chromosomes. Cell division (mitosis and meiosis). Life cycles. Linkage and recombination in eukaryotes. Bacterial genetics. Gene mapping and tetrad analysis. Genotype and phenotype. Chromosomal changes. DNA: Structure and replication. RNA: Transcription. Rgulation of gene transcription. Gene isolation and manipulation. Genomics. Transposons.  Mutations. Repair and recombination.  Model organisms. Laboratory work: : I. The fruitfly Drosophila melanogaster. II. Mitosis in onions. III. Plasmids and restriction enzymes. IV. PCR. V. Analysis of asci from Sordaria fimicola.

Exam: Laboratory and problems 25%, written 75%. Minimum mark needed for each part.

The cell biology part includes four lectures each week for 14 weeks (4L week for 14 weeks). The content includes: Introduction to cell biology, structure and evolution of eukaryotic cells. The main emphasis is on eukaryotic cells. Chemistry of the cell and energy conversion, structure and function of cellular macromolecules. The structure and function of cellular organs and functional units like the cell membrane, nucleus, mitochondria, chloroplasts, cytoskeleton, golgi-system, lysosomes and peroxisomes. Intracellular regulation and signal pathways linked to communication between cells, together with cell differentiation and cancer. Details on extracellular matrix are included and basic immunology.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

The aim of the course is:- To give students overview of processes in materials engineering;- To encourage students to think about feasible ways to utilize renewable energy. The course will cover the industrial processes in some of the larger Icelandic companies, including the production of ferro-alloys, aluminium smelting, rockwool production, recycling of steel, algea and diatomitemining, and production of sodium chlorine, fertilizers, cement. The course will also cover some of the larger material engineering processes that are not in practice in Iceland but may be a feasible option for Icelandic industry. Students will get good overview of the processes, required materials, source of power and power consumption, pollution, products etc. Discussions will be held on the financial background for individual processes, covering aspects such as production cost, profit and the influences of market share changes. Grades are based on 2 larger projects the students work on through the semester. Field trips are an important part of the course.

The objective of the course is to teach the fundamental principles of materials science so the student can better understand material behavior and select appropriate materials for a given application. Theoretical basis is given for the understanding of material behaviour from a microscopic view. The course includes the following topics: crystalline structures, imperfections, diffusion, mechanical properties, deformation and strengthening mechanisms, fracture and fatique, phase diagrams, phase transformations, thermal processing of metal alloys, types of materials (metal alloys, polymers, ceramics, composites), corrosion and degradation of of materials. The course includes homework problems and practical classes in laboratory.

Basic thermodynamic and electrochemical principles that cause corrosion. Procedures of electrochemical measurements used to investigate corrosion behavior. Methods of corrosion protection and prevention, materials selection and design.

The course is taught every other year on even numbered years.

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.

Objective:
To participate in the international Formula Student project by designing and building an electric race car with the purpose of participating in international competitions amongst universities. Strict requirements must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part A is the project preparation, planning and technical design.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

x

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).

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.

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.

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.

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.

Introduction to processes and material and energy balance calculations applied to industrial processes. Analysis of gas behavior, gas-liquid systems, and phase equilibrium. Material balances, including reaction systems and multiple-unit systems. Energy balances, including reaction systems and multiple-unit systems, and combined energy-material balances.

A systematic introduction to the use of process simulators (like Aspen) to model, design and optimize chemical manufacturing processes. The selection, optimization and combination of reactors, separation equipment and heat exchangers. An introduction to the concepts and principles of project economics.

This course provides an introduction to the design and analysis of chemical reactors, including batch, plug flow, continuous stirred tank reactors, and bioreactors. It covers key concepts in chemical thermodynamics, reaction kinetics, and catalysis, enabling students to develop a strong foundational knowledge in chemical reaction engineering. The course also includes guest lectures from industry experts and student presentations, fostering a connection to real-world applications.

In this course, the main metabolic processes of cells are studied, with a focus on carbohydrate, fat, and protein metabolism, as well as the metabolic regulation of these processes. The course begins with a detailed examination of carbohydrate metabolism, including glycolysis (both aerobic and anaerobic), the citric acid cycle, and the pentose phosphate pathway. Then we continue into pathways such as gluconeogenesis, glycogen breakdown, and then into how carbohydrate metabolism is regulated.

Next, the focus shifts to fat metabolism, where the breakdown of triglycerides, fatty acid oxidation, and fatty acid synthesis are explained. Special emphasis is placed on the regulation of fat metabolism and the control of enzymes involved in these processes. Following this, protein metabolism is addressed, where protein hydrolysis, amino acid degradation, and the urea cycle are studied.

The course also covers the integration and regulation of metabolic pathways, with a focus on the complex regulation that occurs in the key steps of these pathways, considering both intracellular signals and hormones. It examines how these processes adapt to various conditions to maintain homeostasis and the effects of disruptions in their regulation. Lastly, photosynthesis and the Calvin cycle are covered.

This course is highly beneficial for those seeking an in-depth understanding of biochemical processes and the biochemistry of the human body.

Lectures are held twice a week (2 x 40 minutes) over 13-14 weeks. 

During this course, students will be introduced to organisms and acellular entities too small to be seen by the unaided eye.  They can acquire knowledge on the characteristics of bacteria, archaea, viruses and eukaryotic microorganisms.  The course will explain the importance of microorganisms, how they live in diverse and dynamic ecosystems and how some affect humans, for example by being valuable for the food industry or by causing disease.  The students will gain laboratory experience and practice aseptic techniques. 

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.

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

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Systems biology is an interdisciplinary field that studies the biological phenomena that emerge from multiple interacting biological elements. Understanding how biological systems change across time is a particular focus of systems biology. In this course, we will prioritize aspects of systems biology relevant to human health and disease.

This course provides an introduction to 1) basic principles in modelling molecular networks, both gene regulatory and metabolic networks; 2) cellular phenomena that support homeostasis like tissue morphogenesis and microbiome resilience, and 3) analysis of molecular patterns found in genomics data at population scale relevant to human disease such as patient classification and biomarker discovery. In this manner, the course covers the three major scales in systems biology: molecules, cells and organisms.

The course activities include reading and interpreting scientific papers, implementation of computational algorithms, working on a research project and presentation of scientific results.

Lectures will comprise of both (1) presentations on foundational concepts and (2) hands-on sessions using Python as the programming language. The course will be taught in English.

Mechanical systems and mechatronics system elements. Mechanism, motors, drives, motion converters, sensors and transducers. Signal processing and microprocessor.

In this course students are introduced to the basic concepts and methods for parametric representation of curves such as the Bezier-, Hermite- and NURBS curves.  Students will learn about the methods for representing three-dimensional wireframe-, solid- and surface models.  The course will cover the use of parameters when developing and creating three-dimensional modeling, the creation of assembly drawings using mating operators and how different engineering software solutions can communicate. 

The course provides a good fundamental overview of the available engineering software solutions – their advantages and limitations – and the students will learn about the current trends in their field, e.g. in the analysis, simulation, prototyping and manufacturing.  The current trends will be indroduced through guest lectures, company visits and a mini-seminar where the students write articles and present new and exciting research or new techniques (based on peer-review papers). 

Concurrently with the lectures, students work on an unstructured engineering project where they will engineer and build a working prototype, write the results in a report and present the results.

Goal: Enable the students to: 1: Study thermodynamics from the viewpoint of the second law of thermodynamics 2. Understand standard power cycles, and their use for analysis of power plants 3. Understand air conditioning systems and their necessity 4. Understand thermochemistry and be able to estimate heat release through combustion. Content: Work, heat and energy conversion. Exergy and anergy. Energy, energy price and energy quality. Standard power and refrigeration cycles. Steam power cycles, geothermal utilization. Gas mixtures, moist air, ventilation and air purifiers. The Mollier i-x chart. Thermochemistry, combustion and reactions, chemical equilibrium. New energy systems. Exercises, design project.

Heat conduction, one and two dimensional systems, steady and unsteady heat conduction, numerical analysis of heat conduction systems. Fins and enlarged heat transfer surfaces. Heat transfer by convection, laminar and turbulent flow. Free and forced convection. Evaporation and condensation. Thermal radiation, Stefan-Boltzmann's and Planck's laws. Thermal radiation properties of materials. Shape factors, radiative heat exchange between surfaces, radiation properties of gases. Heat exchangers and their design. Special topics in heat transfer.

To participate in the international Formula Student project by designing and bulding an electric race car with the purpose of participating in international competitions amongst universities. Strict requirement must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part B is the construction of the car and preparing of participation in the international student competition.

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. 

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.

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.

Basics of linear algebra over the reals.  

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

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.

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 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.

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.

Order of magnitude estimates, scaling relations, and dimensional analysis. Plotting with matplotlib. Complex numbers, oscillations and Fourier-series. Mechanics and the time derivatives of vectors. Particle trajectories in polar coordinates. Derivatives, the chain rule and equations of state. Scalar and vector potentials and connection to electromagnetism. Stokes and divergence theorems and Maxwell's equations. We emphasize applications and problem solving.

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.

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 quantum mechanics. 

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

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.

Python tools related to general data and time series analysis. The method of least squares, linear and non-linear fitting. Fourier transforms, fast Fourier transforms (FFT), spectral analysis and convolution. Differential equations, including the Laplace equation 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.

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.

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.

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.

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.

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 Microscope (SEM), and Transmission Electron Microscopy (TEM). Scaling of transistors, MOSFET, and finFET. Carbon Nanoscructures, Graphene and Carbon nanotubes. Lithography. Nanostructured Ferromagnetism. Nano-optics,  Plasmonics, metamaterials, cloaking and invinsibility. Molecular Electronics.

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

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

Minimum number of students registered for the course to be taught: 10

This course will cover basics in intellectual property rights with emphasis on patents. What is intellectual property and when and how can they best be protected? How does intellectual property rights work (e.g. patents), and how can they be used and applied in innovation and industry. The system‘s organization will be covered, as well as the patent process, making a financial plan relating to patents, and database searches.

x

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.

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.

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 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.

The objective of the course is that students get the skills to:

1.    Understand the main concepts in accounting, cost theory and investment theory.

2.    Be able to use methods of measuring the economic feasibility of technical projects.

3.    Be able to develop computer models to assess the profitability of investments, the value of companies and pricing of bonds

Among topics included are accounting, cost theory, cash flow analysis, investment theory, measures of profitability including net present value and internal rate of return, and the building of profitability models. The course ends with a group assignment where the students exercise the development of computer models for feasibility assessment of projects.

The course is an introductory course in project management. It introduces key concepts of project management and covers context and selection of projects, project planning, project monitoring, management of project teams, and project closure. Students create and execute project plans in groups. Special emphasis is on using of project management for managing technological innovation in organizations.

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 thorough treatment of the fundamentals of biochemistry - part one; structure and function of macromolecules. The scope of biochemistry. Water and its properties. Interactions in biomolecules. Amino acids, peptides and the structure of proteins. Protein function.  Protein stability, folding, and dynamics related to function. Carbohydrates and glycobiology. Lipids, membranes and membrane proteins. Enzyme kinetics, regulation of enzyme activity, and mechanisms of enzyme catalysis. Signal transduction and membrane receptors. Structure of nucleic acids, stability, and basic recombinant technology. Final grade is combined from the final exam (85% ) and a midterm exam (15%).

Lectures:
Twice weekly (2 x 40 min.) Probelm solving class (2 x 40 min.) weekly.

Course evaluation:
Final exam (3 hours): 85% of final grade.
Midterm: 15% of final grade.

Textbook:
Nelson D.L. & Cox M.M. Lehninger: Principles of Biochemistry, 8th Edition, 2021

Lectures: Mendelian inheritance. Sex chromosomes. Cytoplasmic inheritance. Chromosomes. Cell division (mitosis and meiosis). Life cycles. Linkage and recombination in eukaryotes. Bacterial genetics. Gene mapping and tetrad analysis. Genotype and phenotype. Chromosomal changes. DNA: Structure and replication. RNA: Transcription. Rgulation of gene transcription. Gene isolation and manipulation. Genomics. Transposons.  Mutations. Repair and recombination.  Model organisms. Laboratory work: : I. The fruitfly Drosophila melanogaster. II. Mitosis in onions. III. Plasmids and restriction enzymes. IV. PCR. V. Analysis of asci from Sordaria fimicola.

Exam: Laboratory and problems 25%, written 75%. Minimum mark needed for each part.

The cell biology part includes four lectures each week for 14 weeks (4L week for 14 weeks). The content includes: Introduction to cell biology, structure and evolution of eukaryotic cells. The main emphasis is on eukaryotic cells. Chemistry of the cell and energy conversion, structure and function of cellular macromolecules. The structure and function of cellular organs and functional units like the cell membrane, nucleus, mitochondria, chloroplasts, cytoskeleton, golgi-system, lysosomes and peroxisomes. Intracellular regulation and signal pathways linked to communication between cells, together with cell differentiation and cancer. Details on extracellular matrix are included and basic immunology.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

The aim of the course is:- To give students overview of processes in materials engineering;- To encourage students to think about feasible ways to utilize renewable energy. The course will cover the industrial processes in some of the larger Icelandic companies, including the production of ferro-alloys, aluminium smelting, rockwool production, recycling of steel, algea and diatomitemining, and production of sodium chlorine, fertilizers, cement. The course will also cover some of the larger material engineering processes that are not in practice in Iceland but may be a feasible option for Icelandic industry. Students will get good overview of the processes, required materials, source of power and power consumption, pollution, products etc. Discussions will be held on the financial background for individual processes, covering aspects such as production cost, profit and the influences of market share changes. Grades are based on 2 larger projects the students work on through the semester. Field trips are an important part of the course.

The objective of the course is to teach the fundamental principles of materials science so the student can better understand material behavior and select appropriate materials for a given application. Theoretical basis is given for the understanding of material behaviour from a microscopic view. The course includes the following topics: crystalline structures, imperfections, diffusion, mechanical properties, deformation and strengthening mechanisms, fracture and fatique, phase diagrams, phase transformations, thermal processing of metal alloys, types of materials (metal alloys, polymers, ceramics, composites), corrosion and degradation of of materials. The course includes homework problems and practical classes in laboratory.

Basic thermodynamic and electrochemical principles that cause corrosion. Procedures of electrochemical measurements used to investigate corrosion behavior. Methods of corrosion protection and prevention, materials selection and design.

The course is taught every other year on even numbered years.

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.

Objective:
To participate in the international Formula Student project by designing and building an electric race car with the purpose of participating in international competitions amongst universities. Strict requirements must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part A is the project preparation, planning and technical design.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

x

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).

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.

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.

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.

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.

Introduction to processes and material and energy balance calculations applied to industrial processes. Analysis of gas behavior, gas-liquid systems, and phase equilibrium. Material balances, including reaction systems and multiple-unit systems. Energy balances, including reaction systems and multiple-unit systems, and combined energy-material balances.

A systematic introduction to the use of process simulators (like Aspen) to model, design and optimize chemical manufacturing processes. The selection, optimization and combination of reactors, separation equipment and heat exchangers. An introduction to the concepts and principles of project economics.

This course provides an introduction to the design and analysis of chemical reactors, including batch, plug flow, continuous stirred tank reactors, and bioreactors. It covers key concepts in chemical thermodynamics, reaction kinetics, and catalysis, enabling students to develop a strong foundational knowledge in chemical reaction engineering. The course also includes guest lectures from industry experts and student presentations, fostering a connection to real-world applications.

In this course, the main metabolic processes of cells are studied, with a focus on carbohydrate, fat, and protein metabolism, as well as the metabolic regulation of these processes. The course begins with a detailed examination of carbohydrate metabolism, including glycolysis (both aerobic and anaerobic), the citric acid cycle, and the pentose phosphate pathway. Then we continue into pathways such as gluconeogenesis, glycogen breakdown, and then into how carbohydrate metabolism is regulated.

Next, the focus shifts to fat metabolism, where the breakdown of triglycerides, fatty acid oxidation, and fatty acid synthesis are explained. Special emphasis is placed on the regulation of fat metabolism and the control of enzymes involved in these processes. Following this, protein metabolism is addressed, where protein hydrolysis, amino acid degradation, and the urea cycle are studied.

The course also covers the integration and regulation of metabolic pathways, with a focus on the complex regulation that occurs in the key steps of these pathways, considering both intracellular signals and hormones. It examines how these processes adapt to various conditions to maintain homeostasis and the effects of disruptions in their regulation. Lastly, photosynthesis and the Calvin cycle are covered.

This course is highly beneficial for those seeking an in-depth understanding of biochemical processes and the biochemistry of the human body.

Lectures are held twice a week (2 x 40 minutes) over 13-14 weeks. 

During this course, students will be introduced to organisms and acellular entities too small to be seen by the unaided eye.  They can acquire knowledge on the characteristics of bacteria, archaea, viruses and eukaryotic microorganisms.  The course will explain the importance of microorganisms, how they live in diverse and dynamic ecosystems and how some affect humans, for example by being valuable for the food industry or by causing disease.  The students will gain laboratory experience and practice aseptic techniques. 

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.

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

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Systems biology is an interdisciplinary field that studies the biological phenomena that emerge from multiple interacting biological elements. Understanding how biological systems change across time is a particular focus of systems biology. In this course, we will prioritize aspects of systems biology relevant to human health and disease.

This course provides an introduction to 1) basic principles in modelling molecular networks, both gene regulatory and metabolic networks; 2) cellular phenomena that support homeostasis like tissue morphogenesis and microbiome resilience, and 3) analysis of molecular patterns found in genomics data at population scale relevant to human disease such as patient classification and biomarker discovery. In this manner, the course covers the three major scales in systems biology: molecules, cells and organisms.

The course activities include reading and interpreting scientific papers, implementation of computational algorithms, working on a research project and presentation of scientific results.

Lectures will comprise of both (1) presentations on foundational concepts and (2) hands-on sessions using Python as the programming language. The course will be taught in English.

Mechanical systems and mechatronics system elements. Mechanism, motors, drives, motion converters, sensors and transducers. Signal processing and microprocessor.

In this course students are introduced to the basic concepts and methods for parametric representation of curves such as the Bezier-, Hermite- and NURBS curves.  Students will learn about the methods for representing three-dimensional wireframe-, solid- and surface models.  The course will cover the use of parameters when developing and creating three-dimensional modeling, the creation of assembly drawings using mating operators and how different engineering software solutions can communicate. 

The course provides a good fundamental overview of the available engineering software solutions – their advantages and limitations – and the students will learn about the current trends in their field, e.g. in the analysis, simulation, prototyping and manufacturing.  The current trends will be indroduced through guest lectures, company visits and a mini-seminar where the students write articles and present new and exciting research or new techniques (based on peer-review papers). 

Concurrently with the lectures, students work on an unstructured engineering project where they will engineer and build a working prototype, write the results in a report and present the results.

Goal: Enable the students to: 1: Study thermodynamics from the viewpoint of the second law of thermodynamics 2. Understand standard power cycles, and their use for analysis of power plants 3. Understand air conditioning systems and their necessity 4. Understand thermochemistry and be able to estimate heat release through combustion. Content: Work, heat and energy conversion. Exergy and anergy. Energy, energy price and energy quality. Standard power and refrigeration cycles. Steam power cycles, geothermal utilization. Gas mixtures, moist air, ventilation and air purifiers. The Mollier i-x chart. Thermochemistry, combustion and reactions, chemical equilibrium. New energy systems. Exercises, design project.

Heat conduction, one and two dimensional systems, steady and unsteady heat conduction, numerical analysis of heat conduction systems. Fins and enlarged heat transfer surfaces. Heat transfer by convection, laminar and turbulent flow. Free and forced convection. Evaporation and condensation. Thermal radiation, Stefan-Boltzmann's and Planck's laws. Thermal radiation properties of materials. Shape factors, radiative heat exchange between surfaces, radiation properties of gases. Heat exchangers and their design. Special topics in heat transfer.

To participate in the international Formula Student project by designing and bulding an electric race car with the purpose of participating in international competitions amongst universities. Strict requirement must be followed to participate and this will give the students valuable experience in designing and implementing practical solutions to difficult engineering problems, which is the main objective of the project.

Part B is the construction of the car and preparing of participation in the international student competition.

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.