I term (6+6)

The basic concepts of the set theory; relations; functions; algebraic structures. Vactor spaces; systems of linear equations; matrices. Linear transformations of finite-dimensional vector spaces; the transitions between various bases. Vectors in the real space; operations in the set of vectors. Analytical geometry, straight line and plane in space.

The basic properties of the real line and real functions. Sequences, limits of functions, continuity, differentiability. Important theorems: Rolle?s, Lagrange?s, Taylor?s theorem. Examiningof functions. Indefinite and definite integral. The application of definite integral. Improper integral.

II term (4+4)

The space Rn, real functions of several real variables, limits and continuity. Partial derivatives, differentiability. Mean value theorems. Conditional extremes. Theorems on impicit functions.

Introduction to vector analysis. Vector function of one, two and three variables. Curves and surfaces. Multiple integrals. Change of variables and the calculation of multiple integrals. Surface and line integral. The theorems of Green, Ostrogradskii-Gaus and Stokes. Independence of the line integral on the integration path.

Numerical series, criteria for the absolute convergence, conditional convergence. Functional series, the properties of power series. Series expansion of functions. Summing of power series.

Functions defined by definite and improper integrals. Contuinuity. Derivation by the parameter, the change of order of integration.

III term (4+4)

Operations with complex numbers. The functions of complex variable, Euler formula. The derivative of function of complex variable, analytical functions. Conformal mapping of the analyti function; Zhukovski function.

Cauchy?s integral theorem and formulae. Applications.

Complex sequences and series. Taylor and Maclaurin series. Singularities of the analytic function. Residue theory and its application for the evaluation of integrals. Analyti continuation. Analytic continuation by power series. Global analytic function.

First order differential equations: Picard and Lindelof theorem, the method of successive approximations. Elementary mathods of solving: separation of variables, homogenious linear, Bernoulli?s, the equation of total differential, integration factor. Implicit equations, the general procedure of parameter introduction.

Linear equations of n-th order. Homogenious linear equation; the forming of the solution. Non-homogeneous equation, method of constant variation. Homogeneous and nonhomogeneous equation with constant coefficients. Method of equal coefficients. Euler?s equation. Power series solution. Frobenius method (regularly singular points). The boundary problem. The system of differential equations. Homogeneous and nonhomogeneous linear systems. Linear systems with constant coefficients.

The basic notions and types of solutions of the first and second order partial differential equations. Partial differential equations of the first order: homogeneous and nonhomogeneous. Lagrange?s theory of integrals. Lagrange-Charpit method for the determination of complate integral.

(PROBABILITY AND MATHEMATICAL STATISTICS)

IV term (2+2)

Experiments with random outcomes. Random events. Operation in the field of events. Probability. Conditional probabilities, independence and Bayes? formula. Random variables of discrete and continuous type. The functions of random variables. Multidimensional random variables; marginal distributions and the density function of probability distribution. Conditional distributions and independence of random variables. Mathematical expectation and its properties, variance of the random variable and properties. Correlation coefficient. Moments of the random variable. Median and mode of the random variable. Regression and linear regression. Entropy and information: basic concepts of Shanon?s information theory. The law of large numbers. Central limit theorem. Population. Random sample. Statistics. Central theorem of the statistics. Some distributions important in mathematical statistics. The theory of estimations: centered (unbiased) and efficient estimation. Maximum likehood method, the method of moments. Interval of confidence for mathematical expectation and variance. The hypothesis testing; mathematical expectation, variance, correlation coefficient. Nonparametric Pearson?s Chi-square test. Contigency tables.

I term (3+3)

Introduction to chemistry. The laws of chemical bonding. Mole. Classification of elements and inorganic compounds. Electronic structure of the atom and the chemical bond. Molecular structures. Electronegativity. Metalic bond. Hydrogen bond. States and structure of pure substances. Vapour pressure and state diagram. Energy changes in chemical reactions. Free energy and spontaneous processes.

Rate of a chemical reaction. Molecularity and reaction order. Activation energy. Catalysis. Chemical equilibrium. Solutions. Colligative properties of solutions. Equillibrium processes in solutions of acids and bases. Oxidation and reduction. Electrode potential. Galvanic elements. Corrosion. Electrolysis. Explosives. Rocket fuels.

PROGRAMMING AND NUMERICAL MATHEMATICS

IV term (3+4)

Classification and description of computers. Program support. System and application software. Operating systems. Text processors. Application software specialized for solving mathematical and statistical problems. Programing languages.

Theory of errors. Interpolation. Least square method. Regressin and empirical expression. Numerical integration and derivation. Solution of the systems of linear and nonlinear equations. Numerical solving of ordinary and partial differential equations.

I term (1+1)

The role of the experiments in the physical research, principle of performing the physical experiments. The technique of the physical experiment. Measures and units of physical quantities, systems of units. The history of measurements and units, International system. Dimensional analysis. The representation of the results of the experiments. Operation with approximate numbers. Interpolations, extrapolations.

Probability and statistics. The general properties, the distribution of the error propagation. Special distributions: binomial, multinomial, Poissons, uniform, normal, exponential, Chi-distribution, Student-distribution. Intervals of confidence. The comparison of experimental data with the theory, rejecting of bad measurements, statistical errors, systematic errors, detection efficiency, superposition of functions, probability density. The estimate of the parameters. Maximum likelyhood method. Last square method. Method of the moments. Minimization process. Test hypothesis, quality of the fit and consistency test.

II term (6+6)

The aims and the experimental method in physics. Physical quantities and their measurements. Kinematics of the point mass and rigid body. Rotational motion of the rigid body. Newton?s laws of motion. Frictional forces. Dynamics of free and constrained point mass. Galileo?s principle of relativity. Noninertial reference frame. Rigid body dynamics. Gyroscopic effect. Gravitation. The fundamentals of the special theory of relativity. Mechanics of continuum. Elasticity. Fluid mechanics.

Mechanical oscillations. Superpositions of harmonic oscillations. Damped and forced oscillations. Resonance. Propagation, equation and properties of the mechanical waves. Sound waves. Objective and subjective characteristics. Doppler?s effect.

III term (4+5)

Basic characteristics of the systems of molecules. The foundation of the molecular-kinetic theory. Temperature (the zeroth law of thermodynamics and methods of temperature measurements). Molecular velocity distribution after Maxwell. Molecular collisions. Mean free path of the molecule. Boltzmann?s distribution. Transport phenomena (therma conduction, viscosity, diffusion in gases). The subject and the methods of thermodynamics. Joule?s and Joule-Thompson?s experiment. Enthalpy. Processes in gases. Ideal heat engines. Carnot?s cycle. The second law of thermodynamics. Clausius? theorem. Entropy. Maxwell-Boltzmann statistics. Microstates and macrostates. Thermodynamic probability. Entropy and probability. Real gases. Intermolecular forces. Potential of the intermolecular interaction. Transition from gaseous to liquid state. Phase transitions. Van der Waals equation. Compression of gases and achivement of low temperatures. Nerst? theorem. The structure of liquids. Liquid solutions.

III term (4+6)

Electric induction. Proof of two kinds of charge. Coulomb?s law. Electric field. Gauss? theorem. Electric dipole. Electric potential. Effects of peaks. Capacutance. Capatitors. Dielectric polarization. Ferroelectric and piezoelectric properties of crystals. Refraction of the field in dielectrics.

Electric current. Electric resistance. Superconductivity of metals, alloys and ceramic materials. Application of superconductivity. Free electrons motion in metal. Kirchoff?s rules. Measurement of the electromotive force. Electric measuring instruments. Work and power of electric current. Thermoelectric phenomena. Magnetic field of the electric current. Lorentz force. Hall?s effect. The action of the magnetic field to current carrying conductor. Magnetic field of the moving charged particle. Magnetic properties of the materials. Electric current in the electrolytes. Electrolysis. Farraday?s laws of electrolysis. Batteries. Electric current in diluted gases, Volta?s arc. Electric current in the vacuum. The determination of the specific charge of the electron.

Electromagnetic induction. Mutual induction and self-induction. Eddy currents. Magnetic hysteresis. Alternating currents. Impedance. Symbolic calculation in electrical engineering. Voltage resonance in RLC circuit. Power of alternating current. Dynamo and three-phase generator. Rotating magnetic field. Asynchronous motor transformers. Electric energy transfer. Electromagnetic oscillations.

IV term (4+5)

Maxwell?s equations. The spectrum of electromagnetic waves. Light sources. Astronomic and laboratory methods of measuring the velocity of light. Photometry. reflection of light. Refraction of light and refraction index. Total reflection. Optical fiber and its application in medicine and telecommunications. Atomic and molar refraction. Fermat?s principle. Refraction through prism. Normal and anomalous dispersion. Relative and angular dispersion of the prism. Abbe?s prism. Achromatic prism. Determination of the refraction index. Phase and group velocity.

Reflaction and refraction on spherical surfaces. Spherical mirrors. Thin and wide lenses. Systems of lenses. The determination of the lens focal length and lens deficiencies. The eye. Microscope.

The concept of coherence. Light interference. Interference at thin planparallel plate. Interferometers (Fabry-Ibert, Jamin and Michelson). Newton?s rings. Application of the interference for the determination of the quality of optical surfaces. Polarization of light. Optical properties of the materials. Double refraction. Nicol prism. Polaroids. Elliptic and circular polarization. Artificial anisotropy. Kerr?s effect. Optical activity.

Thermal radiation. Optical pyrometer. Luminescent radiation. Quantum phenomena in optics. Photoelectric effect. Pressure of light. The discovery and properties of Roentgen radiation. The application of X-rays in medicine, industry and science.

IV term (2+2)

The essentials of linear algebra (a repetion). Vector spaces. Vectors in three dimensions. Transformation of coordinates and vectors during the rotation of the reference frame. Vector algebra.

The notions of the vector analysis. Scalar and vector fields. Gradient, divergence and curl. Integral theorems. Spatial derivatives. Theory of potentials.

Generalized coordinates. Metric form. Lame?s coefficients. Vector calculus in generalized coordinates.

Differential equations of the mathematical physics. Examples of equations in one and three dimensions.

Tensors in three dimensions. The concept and definition of the tensor, transformation law of tensors, tensor invariants. Tensor algebra, special types of tensors. Tensors and matrices. The repetition of matrix algebra. Matrices associated to vectors and tensors. Examples from physics. The normal form of the tensor. Tensor eigenproblem. Hamilton?s equation. Eigenproblem of the symmetric tensor. Afine transformations.

General tensor calculus. Afine space. Scalars, contravariant and covariant vectors, higher rank tensors. Operations with tensors. Metric spaces and fundamental tensor. Euclid space. Associated tensors.

Group theory. Groups, subgroups and classes. Linear representations of groups and characters. Continuous groups. Symmetries in physics - connection with the group theory.

V term (4+4)

theoretical

Basic ideas of mechanics and theory of relativity. The concepts of space and time. Elements of kinematics. The concept of force. The basic dynamical equation. The general law of dynamics.

Constrained motion. D?Allember-Lagrange?s principle. The equations of the free motion. The equations of constrained motion. Lagrange?s equations. Method of generalized coordinates. Hamilton?s principle. Hamilton?s equations. Canonical transformations. System with single degree of freedom. Small oscillations. Central motion. Particle collisions. Kinematics elements of the rigid body. Dynamics elements of the rigid body. The laws of motion of the rigid body. Kinematics of the relative motion. Dynamics of the relative motion. Basic ideas of continuum mechanics. Kinematics of the continuum. Dynamics of the continuum. Basic equations of the elasticity. Oscillations of a string. Kinematics and dynamic elements of the fluid. Differential equations of motion of ideal fluid.

VI term (4+4)

theoretical

Basic ideas of the electrodynamics. Electrodynamics concepts. Integral laws of electrodynamics. Maxwell?s equations for the vacuum. Maxwell?s equations for the material media. Complete system of equations. The consequences of Maxwell?s equations. Electromagnetic potentials. Fast varying fields. Fourier?s method. Energy of the electromagnetic field. Ponderomotive forces and the momentum of the electromagnetic field. Electrostatic field and potential. Energy of the electrostatic field. Diamagnetism and paramagnetism. Para-electricity. Media with dispersion. Propagation of the plane electromagnetic waves. Retarded potentials. The radiation of dipole and multipole. Maxwell?s electromagnetic theory of light. Reflection and refraction of light. Crystal optics. Light dispersion. Electromagnetic field in the cavity. Thermal radiation. Basic ideas of the theory relativity. Lorentz transformations. Geometrical representation of events. Covariant formulation of mechanics. Covariant formulation of vacuum electrodynamics. Transformation law. Charged particle in the electromagnetic field. Covariant formulation of the conservation laws.

V term (4+4), VI term (2+4)

theoretical+experimantal

The atomic composition of the matter and charge. Nuclear structure of atoms, X-rays. The structure of atom and the classical physics. Quantum theory of electromagnetic radiation. Bohr-Sommerfeld theory of atom. Waves and corpuscules. Free particles, particle in the box, linear harmonic oscillator and rotator in the Quantum Mechanics. Hydrogen-like atom in the Quantum Mechanics. Wave model of the atom. Multiplicity of terms and structure of spectra. Term symbols. Zeeman, Paschen-Back, Stark and Stern-Gerlach effect. Hyperfine structure of spectra. Radiation processes. The width of spectral terms and lines. The fundamentals of quantum electronics: stimulated emission of electromagnetic radiation, quantum amplifier and generator, the types of lasers and their application. The structure, the energy and the spectra of di-atomic and multi-atomic molecules. hybridization. The types of covalent bonds and molecular orbitals.

V+VI term (2+4)

theoretical+experimantal

Electronic components. The flow of electric current through various substances. Energy bands in crystals. Pure and doped semiconductors. Free charge carrier concentration out of thermodynamic equillibrium. pn - junction. The current through pn-junction. Realistic semiconductor diodes. Experimental proof of the hole existence. Diode circuits.

Bipolar transistor, tyristor, triac and diac. Field effect transistors. Transistor parameters and equivalent circuits. Amplifying properties of the transistor. Switching behaviour of the transistor. Analogous electronic circuits. Digital electronic circuits. Telecommunications. Radio and television. Integrated circuits.

VI term (3+3)

Abstract spaces: metric, normalized, Hermitean, unitary and Hilbert spaces. Dirac?s notation. Superposition principle and uncertainty principle. Linear operator, matrix representation. Eigenproblem of Hermitian operator. Operators in Quantum Mechanics. Examples.

Special functions. Eigenproblem of the Hamiltonian of free particle. Dirac?s delta-function: definition and properties. Linear harmonic oscillator. Hermite?s polynomials, second quantisation representation, matrix picture. Hydrgen-like atom: center of mass system, eigenproblems of the operators lz and l^2. Legendre?s polynomials and spherical harmonics. Radial part: Laguerre?s polynomials. Quantum numbers and physical characteristics.

Integral transformations: Fourier, Laplace, Melin, Abel. Definition and properties. Application in physics.

Integral equations. Regular integral equations: classification, properties, solving. Eigenproblems of the integral operator. Method of successive approximations and the resolvent. Examples in physics.

Nonlinear integral equations, singular integral equations: functions of the complex variable, improper integral, integral of Cauchy-type, Sahocki and Poincarre-Bertrand formula.

Green?s function in classical mechanics, electrodynamics and quantum mechanics (wave, Poisson and Schroedinger equation).

VII term (4+4)

theoretical

Principles and postulates of quantum mechanics. Schroedinger equation and stationary states. Schroedinger, Heisenberg and interaction picture. Heisenberg equations of motion and correct quantisation of classical systems. Examples of exactly solvable models. Matrix formulation. Quantum mechanical measurement theory. Representation theory. Kinetic moment and moment coupling. Stationary and non-stationary perturbations and variational principle. S-matrix and transition probability. System of indentical particles. Hatree-Fock approximation. Scatering theory. Elastic and inelastic scattering. Scattering of identical particles. Elements of relativistic quantum mechanics. Dirac?s electron theory and electromagnetic field. Interaction of radiation with matter.

VII term (2+2)

theoretical + eksperimental

Gas electronics. Motion of ions and electrons. Ionization and recombination. Ion and electronemission from the solid surfaces. Townsend discharge. Breakdown in gases. Glow discharge. Arc discharge. Gas tubes. Gas discharge based light sources.

Plasma. Plasma parameters. Criteria of the plasma state. Theoretical methods for studying plasma dynamics. Electromagnetic radiation of plasma. Plasma diagnostics.

VII term (2+2)

theoretical + eksperimental

Principles of measuring non-electrical quantities by electrical methods. Measurement of the force. Measurement of the displacement. Methods of measurement of the angular velocity. Transformers for acceleration measurement. Measurement of the pressure. Temperature measurement. Measurement of the fluid velocity and flow. Humidity measurement. Analogous-digital transformers. Digital-analogous transformers.

VII term (2+0) VIII term (2+2)

theoretical

Energetics as a global problem. Energy and conservation laws. I and II principle of thermodynamocs. The availability of the energy transformation. The concept of exergy. Energy and exergy analysis. Fission energy: fission reactors. Fusion energy: fusion reactors. MHD method of energy transformation: MHD generators. Thermoelectric generators. Solar energy. Wind and wave energy. Geothermal energy. Energetics and ecological problems.

VII + VIII term (3+4)

theoretical + eksperimental

The detection of the nuclear radiation. Interaction of charged particles and gamma quanta with matter.

Static properties of the nucleus: composition and dimensions. Symmetries and conservation laws. Nuclear forces: the properties of forces in two-nucleon system. Exchange forces and two-nucleon potential. Meson theory of nuclear forces. Nuclear models. Independent particle model. Collective models. Unified description of the nuclear structure.

Alpha-decay and nuclear potential barrier: energy conditions of alpha-decay. Barrier transparency. The probability of the emission of charged particles. Fission and fusion. Beta-decay and weak interaction: energy conditions of beta-decay. Fermi?s theory of beta-decay. Fermi and Gamow-Teller?s decays. V-A theory. Parity non-conservation in weak interaction. Gamma-transitions in the nucleus. Multipole character of the radiation and the transition probability. Internal conservation. Moessbauer effect. Angular distribution of the radiation.

Nuclear reactions. Particle accelerators. Scattering kinematics. Compaund nucleus. Direct reactions. Nuclear energy. Nucleosynthesis.

Applied nuclear physics: nuclear activation techniques. Dosimetry. Application of radioisotopes in technology and medicine.

VIII term (4+4)

theoretical

Basic ideas and concept of the statistical physics. Distribution functions. Liouville?s equation and theorem. Boltzmann?s transport equation and H-theorem.

Equilibrium statistical physics: Gibbs? ensembles and thermodynamic principles. Thermodynamic potentials. Ideal Boltzmann?s gas. Classical gases with interaction. Quantum statistical operators and ensembles. Information theory and statistical physics. Ideal quantum systems of particles. Bose-Einstein and Fermi-Dirac statistics.

Non-equilibrium quantum ensembles. Linear response of the system and Green?s functions. Quantum systems with interaction. Applications in condensed matter physics. Quasiparticles: phonons, magnons, excitons. Non-ideal Bose gas: 4He superfluidity. Electron-phonon interaction and superconductivity. Irreversibility and kinetic coefficients. The basic kinetic equation.

VII+VIII term (3+4)

experimental

Solid state: matter condensation, ordered state-crystals, partially ordered state-paracrystals, polymers, fibers, amorphous materials.

Crystallography: elements of crystallography, crystallographic methods of material study. Diffraction of radiation on crystals: diffraction of X-rays and other radiation. Experimental diffraction methods.

Crystal structure: physicsl and physico-chemical parameters of crystal structure. Electron states in crystals. Physical properties of solid materials: general properties and reaction to the physical fields. Difference between ordered and disoedered materials.

Behaviour of the materials in the mechanical field, thermal field, electric field, magnetic field and electromagnetic field. Corresponding properties and examination methods.

theoretical

Basic concepts in spherical astronomy. Coordinate systems. Time measuring. Calendar. Planetary motion. Kepler?s laws. The determination of the mass of celestial bodies. The determination of the distances and dimensions of the celestial bodies.

Stars. Internal structure and physical processes within the stars. Star models. Star evolution. Radiation characteristics. Galaxies. Elements of cosmology. Standard cosmological model. Model of the Hot Universe. Inflation model.