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1^st year

MTF009 Modern Physics
Grade: 5

The course gives basic engineering knowledge in nuclear physics, atomic physics, quantum mechanics, X-ray technology, crystal structures, electron theories of solid materials, thermal properties of rigid bodies and temperature radiation. It also provides a necessary basis for more advanced courses within these areas.

Introduction to Unix and e-mail.

Statics: Equilibrium, center of mass, frames, friction,virtual work, stability. Dynamics of particles: Kinematics, work and energy, linear and angular momentum, impact, vibrations. Dynamics of rigid bodies: Kinematics, mass moments of inertia, fixed axis rotation, general plane motion, work and energy, linear and angular momentum.

Introductory classes; planning of experimental work, dimensional analysis, curve fitting of experimental data, error estimation and error analysis. Laboratory work; Two experiments will de performed, lab1 and lab2. The student will work in a small group. The group will work independently without any direct guidance. The results from one experiment will be presented as a report and the results fom the other experiment will be presented at a seminar. An experiment in experimental error handling and analysis will be performed in the same quarter as lab2. A lecture in presentation techniques is given before the students seminar.

The course consists in three parts: basic business administration, managerial economics and accounting. Basic business administration provides an introduction to the field. Managerial economics deals with profitability planning, pricing and capital budgeting. The course part which concerns accounting focuses on the relations between funds flow, profit, and changes in equity.

A complete Calculus-course

2^nd year

MAM057 Vector Calculus and Series
Grade: 5

Vector analysis: Scalar fields, vector fields, line integrals, surface integrals, gradient, divergence, curl, curvilinear coordinates, Gauss's theorem, Stokes's theorem, the scalar potential. Series: Infinite series, convergence, divergence, power series, Fourier series.

Problems concerning ethics of technology are widely discussed in contemporary philosophy of technology. Broadly speaking one may distinguish two perspectives in this discussion, namely an "engineering philosophy of technology" (EPT) and a "humanities philosophy of technology" (HPT). These perspectives are related to different historical traditions in the philosophy of technology. Both have their weak and strong points. While EPT is firmly rooted in the real world of technology, HPT sometimes talks in a shallow way about technology. However, once people who are trained in engineering start reflecting on the nature and meaning of technology they are no longer doing technology but are engaged in a kind of philosophy. Aiming to link engineering and humanity disciplines in an interdisciplinary approach of technology this course will discuss the broad subject ethics and technology both from a HPT (part 1) and an EPT (part 2) perspective. Part 1 will give a profile of modern culture and will show the needs for and possibilities of an ethics for technology. Attention will be focused on two main characteristics of our time: the dominance of technology and the plurality of life styles and moral frameworks. Part 2 will give insight in normative issues coming from technology by analysing the real world of technology, the structure of modern technology and its transforming effects on human life.

Statics: Equilibrium in 3 dim., center of mass, hydrostatics. Dynamics:(Particles and rigid bodies): Kinematics in 3 dim, general equations of motion, laws of conservation, relative motion, coriolis effect, inertia tensor. Special applications: Celestial mechanics (motion of planets and satellites), vibrations, gyroscopic motion.

The course deals with basic concepts in probability and statistics like EDA, the concept of probability, random variables, measure of location and spread, distributions, confidence intervals, and hypothesis testing. Furthermore, is regression analysis (both simple regression and multiple regression) and experimental design dealt with.

In this course, quantum physics is presented by using simple physical situations. The general structure of the mathematical solutions and methods are studied, as well as applications in nuclear physics, atomic physics, molecular physics, and solid state physics. Additionally, in the course is the influence of temperature treated with an emphasis on the Boltzmann factor, which gives relative probabilities for thermal excitations.

Complex functions: Basic concepts, the equations of Cauchy-Riemann, elementary complex functions. Complex integration, Cauchy's theorem, the residue theorem, residue integrals. Laurent series, poles and zeroes. Conformal mapping, bilinear transformations. Harmonic functions. Applications. Theory of transforms: The concept of an integral transform. The Fourier transform, the Laplace transform and the Z-transform. Parseval's relation. Solving differential equations and difference equations with the transform method. Applications.

Case Study - A subject in the area is chosen at the start of the course. The case study shall show connections between technic, politics and enviorenment. Rest of Course - The remaining part of the course is intended to support the case study. The course starts with a presentation of different ways to observe the relationship between man and nature. Our views on nature is considered to have consequenses on the shaping of society, the utilization of technic, and even the system of government. Special attention will be focusde upon democracy as a method of decision. The students will be given an oppurtunity to discuss so called enviorenmental rights and enviorenmental responsabillities, by way of exampel how we as citizens can take responsabillity for the enviorenment. The course will also show the ethical conflicts that can surface when enviorenmental interests clash with other interests.

Vector analysis. Static electric fields, dielectrics. Steady electric currents, conductors. Quasi-static magnetic fields, magnetic materials. Faraday's law of electromagnetic induction. Maxwell's equations. Plane waves.

Fundamentals of the solid state; Atomic bonding and ideal crystal structure. Lattice positions, directions and planes. X-ray diffraction. Diffusion and imperfections in solids. Dislocations and plastic deformation. Binary phase diagrams. Thermal processing of metal alloys. Structural engineering materials. Mechanical properties of metals, ceramics, polymers and composites; strengthening mechanisms and failure. Electronic properties of metals, semiconductors and insulators. Energy levels and bands. The phenomenon of superconductivity. Doped semiconductors and electronic devices. Degradation of materials used in engineering design; Oxidation, corrosion and wear. Materials selection.

Physical models: Derivation of the heat equation, Laplace's equation and the wave equation. Boundary- and initial conditions, uniqueness- and stability conditions, classification, superposition. d'Alemberts formula for the wave equation. Fouriers method: Separation of variables. Eigenfunction expansion methods, the use of Fourier- and Laplacetransforms. Function spaces: Orthogonal projections, convergence in norm, symmetric operators, Sturm-Liouville-operators, generalized Fourier series, Bessel- and Legendrefunctions, distributions.

Hilbert space, Sobolev space, quadratic forms and partial differential equations, Finite Element Method for ordinary and partial differential equations.

The rational and real numbers, the countable and uncountable sets are introduced. Basic topological concepts such as open, closed, bounded and compact sets are introduced. Numerical sequences, series and properties of continuous and differentiable functions are thoroughly discussed. Riemann integral is introduced and its properties are studied. Sequences and series of functions are studied in connection with continuity, integration and differentiation.

General Part (30%) Vector and Tensor Algebra. Analysis of Stress; Mohr's Circles. Kinematics; Deformation, Material Derivative. Conservation Laws. Constitutive Relationships. Fluid Mechanics (35%) Euler's Equation. Potential Flow. Aerodynamic Theory. Compressible flow. Navier-Stokes' Equations. Solid Mechanics (35%) Navier's Equations. Bending and Torsion. Elastic Stress Waves.

Analysis of DC and AC circuits and transients in circuits. Electronic circuits with ideal operational amplifiers. P-Spice.

Crystal structures and interatomic forces. Scattering theory and descriptions of various experimental techniques employed in structure analysis. Heat capacity on the basis of the models of Einstein and Debye. The quantization of the energy of elastic waves in terms of phonos. Lattice waves and the Brillouin zone. Thermal conductivity. The success and failure of the free electron model in accounting for observed metallic properties. The Hall effect and cyclotron resonance. The electronic contribution to heat capacity and thermal conductivity. Energy bands in solids. The nearly free electron model and band gaps. Semiconductor theory and devices. Polarizability. Magnetic susceptibility. The phenomenon of superconductivity. Point defects, dislocations and grain boundaries.

Basic theory for generalized functions The Heaviside function and Dirac's delta functions. Multiplication and differentiation of distributions. Convolution between, and limiting processes of, distributions. Fourier series and Fourier transforms of distributions Periodic distributions and Fourier series. Fourier transforms of distributions. Calculation rules. Physical and Technical interpretations. Applications Solutions of Differential Equations. Green's method. Linear systems.

3^rd year

Numerique
Grade: B+

Arithmétique des calculateurs. Analyse d'erreurs dans les opérations élémentaires. Chiffres significatifs exacts. Équations non-linéaires, méthodes de points fixes et de Newton, ordre de convergence. Systèmes linéaires, factorisation LU, conditionnement et amélioration itérative. Systèmes nonlinéaires. Polynômes d'interpolation, et splines. Différentiation et intégration numérique. Résolution numérique d'équations différentielles, méthodes de Runge-Kutta et de prédiction- correction.

Rappels de la dynamique de Newton. Principe des travaux virtuels et de d'Alembert. Calcul des variations, principe d'Hamilton, coordonnées généralisées et équations de Lagrange. Multiplicateurs de Lagrange. Mouvement à force centrale, stabilité des orbites circulaires. Mouvement oscillatoire, coordonnées normales. Équations d'Hamilton et espace de phase. Théorème de Liouville. Crochets de Poisson. Exemples divers d'application.

Formulation matricielle et applications. Atome d'hydrogène et hydrogénoïdes. Perturbations indépendantes du temps: effet Stark, effet Zeeman. Calculs des variations. Perturbations dépendantes du temps: probabilités de transition, interaction de la radiation avec les systèmes atomiques, diffusion. Systèmes à plusieurs particules, principe de Pauli. Atomes complexes.

Optique géométrique: Principe de Fermat et ses conséquences. Loi de Snell-Descartes et équation du rayon dans un milieu inhomogène. Formation des images: stigmatisme et aplanétisme. Conditions de Gauss: utilisation des matrices. Étude des instruments d'optique. Optique ondulatoire: Ondes monochromatiques et quasi monochromatiques. Cohérences (temporelle et spatiale). Interférences de deux ondes et d'ondes multiples. Diffraction de Fraunhoffer et de Fresnel.

Résolution de problèmes de distribution du champ électrique en présence de conditions aux frontières. Propagation des ondes électromagnétiques planes dans les milieux homogènes. Transfert de puissance, polarisation et atténuation des ondes. Effets d'interfaces: réflexion et réfraction. Réflexion totale et transmission totale. Propagation guidée, guides d'ondes. Lignes de transmission. Charges sur les lignes de transmission. Ondes stationnaires.

Diffusion. Perturbations stationnaires. Atome d'hydrogène : structure fine et hyperfine. Perturbations dépendant du temps. Intégrales de chemin, mécanique quantique relativiste, quantification d'un champ, etc.

Le champ électrique macroscopique. Polarisation, forces, nergie, considerations thermodynamiques. Comportement macroscopique en champ alternatif, pertes, relaxation, résonance, circuits équivalents. Le champ electrique local, les quatre mécanismes de polarisabilité. Équations de Clausius-Mosotti et de Lorentz-Lorenz. Polarisabilité électronique, dispersion anormale. Polarisabilité d'orientation, théories de Debye-Langevin et d'Onsager. Relaxation, les équations de Debye. Diagramme de Cole- Cole et de Cole-Davidson. Les diélectriques solides anisotropes, applications du calcul tensoriel. Piézoélectricitéet ferroélectriciteacute. Méthodes exp rimentales. Applications des diélectriques.

Fonction diélectrique complexe. Dispersion et dissipation des ondesélectromagnétiques. Guides d'ondes. Rayonnement. Formulation covariante de l'électromagnétisme.

Application de l'analyse numérique à des problèmes en physique. Une connaissance de la programmation est nécessaire.

Particules fondamentales : quarks et leptons. Interactions fondamentales : électrofaibles, fortes. Bosons de Jauge et bosons de Higgs. Unification des interactions fondamentales.

4^th year

Applied Mathematics
Grade: 5

Introductory exampels and introduction to the following topics: Dimensional analysis and scaling, pertubation theory, calculus of variation, Hamiltonian theory, Sturm-Liouville theory, partial differential equations, transforms, integral equations, dynamical system, stability and chaos. Analytical and numerical solving methods.

Equvivalent to SMR037:
Introduction: Examples of modern control systems. Terms and definitions. Dynamic Models: Differential equations of physical systems. State -space representations. Linearization and scaling. Dynamic Response: The Laplace transform. Block diagram models. Steady-state errors. Computer-aided control systems design. RegSim - an interactive simulation program. Feedback Control: Properties of Feedback. Steady-state Tracking. PID-controllers. Anti-windup compensation. Stability. Stability criterions. The Frequency-response Design Method: The Bode plot technique. Stability and stability margins. State-space Design: Canonical forms. Control Law. Estimators. Integral control. Digital Control: Digitization. The transfer function of sampled-data systems. The z-transform. Translating of analog design. Discrete design. Hardware characteristics. Sampling-rate selection.

The structure of atoms and molecules, interaction with electric and magnetic fields, radiation and scattering processes. Spectroscopical methods as applied in research and industrial and environmental laboratories, utilizing X-rays, photo electrons, magnetic resonance (ESR and NMR), microwaves and light (IR, visible, UV and Raman scattering). Laboratory exercises to accompany the therotical course.

The basic properties of quarks, elementary particles and atomic nuclei, and of forces and reactions between them, is the central theme of the course. Experimental methods, detectors and large-scale laboratories are described. Among the detailed themes are: Strong, weak and electromagnetic interactions. Static properties of particles. Collisions and decays. Quarks and the quantum chromodynamic theory. Unification of forces in Nature. Large-scale research programmes. Astroparticle physics. The physics front-line. Challenges for the future. The structure of nuclear matter. Potential models for nuclei. Nuclear reactions and radiation. Fission and fusion. Exotic nuclei and quark effects. Quark-gluon plasmas. Nucleosynthesis in stars, supernovas and the early Universe. The course will end with a visit to a Swedish or Central European research centre for particle and nuclear physics (if interest and financing permit).

States of a system, the ergodic assumption, partition function, entropy, micro-canonical, canonical and grand-canonical ensembles, temperature, reversibility kinetic gas theory, Maxwell-Boltzmann distribution, Gibbs distribution, Fermi and Bose statistics, Mean field theory, critical exponents, scaling theory, Monte-Carlo simulations, diffusion, Brownian motion.

Defects in semiconductors. Density Functional Theory, Hartree-Fock, Group theory.

The structure and development of the whole universe, galaxies, stars and solar systems are the central themes of the course. Experimental methods, detectors and various space missions are described. Special weight is given to so-called astroparticle physics, i.e. the coupling between the structure of universe and the properties of elementary particles in particular, when discussing the early Universe. In this respect, the course is also a natural continuation of the course in particle and nuclear physics. Many new, and not so well understood, phenomena will be discussed, such as galactic dark matter, quasars, gamma-ray bursts, neutron stars, the missing solar neutrinos, the cosmic background radiation and MACHOs. Among the homework assignments, one will be the writing of an essay and another a small "research" project.

Einstein's postulates for special relativity. The concept of a four-dimensional space-time. Definitions of measurements of time, distances, masses etc. Causality. Cartesian tensors and tensor formulations of natural laws. Translations and rotations in space-time, and their connections to the conservation laws of Nature. Translation laws for velocities, accelerations, masses etc. The classical and ultra-relativistic approximations. Specific effects, e.g. length contraction, time dilation, relativistic Doppler shift. Conceptual difficulties and "paradoxes" (e.g. the Twin Paradox). Philosophical questions. The ideas behind Einstein's general theory of relativity. Curved space-time and tensors in non-Euclidean space. The four-momentum tensor and Einstein's law of gravitation. Gravitation and cosmology. The curved and expanding Universe. Difficulties and efforts to generalise Einstein's theory.

The course comprises two parts. The first is based on the following chapters in Gåsvik "Optical metrology": 1. Basics. 3. Interference. 4. Diffraction. 6. Holography. 7. Moiré-techniques. 8. Speckle methods. 9. Photoelasticity and polarized light. Demonstrations given are, Diffraction, Optical filtering, Schlieren, Shadowgraph, TV-holography, Sheaography. Depending on the number of participants, laboratory and/or project work within the areas mentioned above is The second part is of a more fundamental nature and includes Fresnel-Kirchoff's theory for the propagation of scalar waves. This theory forms the basis for the treatment of Fresnel- and Fraunhofer diffraction, the propagation of laser beams, Fourier optics and coherence. Polarisation and birefringence is treated with matrix methods. Laboratory work on diffraction and Fourier optics is included.

General relations for the absorption of light. Electromagnetic fields in dielectric materials. Atomic aspects of the laser. Electromagnetic properties of metals. Function and manifacture of semiconductor components, diods, transistors, laserdiods, and CCD elements.

Lie groups and algebras: groups, Lie groups, symmetry groups for differential equations, Lie algebras. Differential geometry: differential equationer, differentiable manyfolds, vector fields.

Kursen omfattar tillämpningar av kemisk termodynamik, elektrokemisk jämvikt, termodynamiska tillståndsfunktioner, aktivitet, kolligativa egenskaper, molekylers absorption av elektromagnetisk strålning samt relationer mellan mikroskopiska och makroskopiska tillstånd. Därvid behandlas molekylers energiegenvärden, urvalsregler, tillståndssummor, kemiska reaktioner i jämvikt samt ideala och icke -ideala lösningar. I avsnittet kemisk kinetik behandlas reaktioners ordning, aktiveringsenergi och reaktionsmekanism. Teorin tillämpas vid räkneövningar och laborationer.

Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught.