SHORT COURSE DESCRIPTIONS OF ENGINEERING PHYSICS
 
Compulsory Courses
  1. Mathematics (B) I.
  2. Mathematics (B) II.
  3. Mathematics (B) III.
  4. Mathematics (B) IV.
  5. Functional analysis
  6. Linear algebra
  7. Linear algebra practice
  8. Numerical methods
  9. Numerical methods practice
  10. Mathematical methods in Physics
  11. Mathematical methods in physics practice
  12. Programming (Pascal)
  13. Digital technology
  14. Electronics I.
  15. Electronics II.
  16. Electronics laboratory practice I.
  17. Electronics laboratory practice II.
  18. Methods of measurements
  19. Chemistry I.
  20. Chemistry II.
  21. Experimental physics I.
  22. Experimental physics II.
  23. Experimental physics III.
  24. Experimental physics practice I.
  25. Experimental physics practice II.
  26. Environmental and radiation protection
  27. Experimental nuclear physics
  28. Mechanics
  29. Mechanics practice
  30. Hydrodynamics
  31. Electrodynamics and theory of relativity
  32. Electrodynamics and theory of relativity practice
  33. Quantum mechanics
  34. Quantum mechanics practice
  35. Statistical physics
  36. Statistical physics practice
  37. Solid state physics I.
  38. Solid state physics II.
  39. Solid state physics practice
  40. Nuclear and particle physics I.
  41. Nuclear and particle physics II.
  42. Optics I.
  43. Atomic and molecular physics
  44. Laboratory in physics I.
  45. Laboratory in physics II.
  46. Laboratory in physics III.
  47. Laboratory in physics IV.
  48. Laboratory in physics V.
  49. Economics
  50. Industrial management and business economy

Compulsory Facultative Professional Courses
(they are not module courses)  

  1. Photonical devices
  2. Optics II.
  3. Macromolecules
  4. Nonlinear oscillations
  5. Quantum mechanics II.
  6. Selected chapters in Quantum mechanics
 

Compulsory Facultative Courses 

  1. Technical use of computers
  2. Taxation, accounting, social insurance
  3. Management for engineers
  4. Technical reliability of production systems, quality regulation
  5. Managing technological changes
  6. Ergonomy
  7. General technical language (English, German, French, Russian)
  8. Special know ledges of technical language (English, German, French, Russian)
  9. Engineering ethics
  10. Technical law
  11. Environment economy
  12. Chapters in history of physics
 
 
Compulsory Courses 

Mathematics (B) I.
Credits: 7
Course director: Dr. Éva V. Nagy
Course description: Basic concepts in set theory and in logic, concept of operation. Brief review of concept of numbers, real numbers, complex numbers. Vectors in 2 and 3 dimensions. The 3 dimensional vector geometry. Operations with vectors. Equations of planes and lines.
Convergence of sequence of numbers and series. The concept of function. Operation between functions. Functions of one variable: definition of limits and continuity. Theorems related with continuity. Differentiability and derivative, tangent. Derivation rules. Analysis of functions. Extreme value problem. Important elementary functions. Approximate solution of equations. Contact of curves. Taylor's formula. Determination of curves by parameters and polar co-ordinates.
Integrals. Riemann-integrability. Integrable functions. Definite and indefinite integral. Concept of primitive function, Newton-Leibniz rule. Rules of integration. Applications of integral calculus (counting the area), curve length. The improper integral. Numerical integrals. Application: separable differential equation.

Mathematics (B) II.
Credits: 7
Course director: Dr. Péter Moson
Course description: Matrices, rank of a matrix, determinants. Invertibility of a matrix. Solution of system of linear equations. Gauss method. Eigenvalue and eigenvector of a matrix. Symmetric matrix. Concept of linear space: space of n-tuples. Base, dimension, base transformation. Euclidean space, scalar product, orthogonal base, theory of principal axis. Quadratic forms. Linear operator (tensor), eigenvector. Applications to linear differential equations. Sequences and series of functions. Limit function, sum function, uniform convergence. Power series, radius of convergence. Taylor series, test of convergence. Fourier series, the feature of the minimizing property of the Fourier polynomial.
The concept of function of several variables (scalar-vector function), continuity. Partial derivatives, differentiability, gradient. Differential. Higher order partial derivatives. Chain rule. Mean value theorems. Directional derivative. Conditional and nonconditional extreme values. Method of least squares. Implicit and inverse function systems. The concept of multiple integral. The geometric meaning of double and triple integral. Integrals with parameters. Multiple integral on normal domain. Transformations of integrals (polar, cylindrical and spherical co-ordinates). Applications.
Vector-scalar functions. Curve length of a space curve. Curvature, torsion. Determination of surface, tangent plane. Area of a piece of surface.

Mathematics (B) III.
Credits: 6
Course director: Dr. Péter Moson
Course description: Differentiability of vector-vector functions. Surfaces given by r(u,v) function. Tensor of derivative and its invariants. Line and surface integrals of vector- vector functions. Divergence and rotation. Theorems of conversion of integrals (Gauss, Stokes, Green). Elements of potential theory. Exact differential equations.
Complex functions. Continuity, differentiability. Cauchy-Riemann equations. Conform transformation. Regular complex function. Complex line integral. Theorem of Cauchy. Cauchy integral formula. Complex potential and its application. Taylor's formula and Laurent series. Complex and real form of Fourier series. Fourier- and Laplace transformation. Systems of ordinary differential equation. Initial value and boundary value problems. Theorems on existence and uniqueness. Systems of linear differential equation. The structure of the general solution. Autonomous differential equations. Stability. Approximative methods of solution. Second order linear partial differential equations. The differential equation of vibrating string. Laplace equation. Linear heat conduction. The solution of initial and boundary value problems with Fourier methods. The application of Laplace transformation for solving of differential equations.

Mathematics (B) IV.
Credits: 4
Course director: Dr. Tamás Szántai
Course description: The concept of probability. Axioms. Combinatorial and geometrical methods. Conditional probability, independence of events. Theorem of total probability, Bayes theorem, multiplication rule. Random variables and their characteristics. The feature of distribution function. Discrete and continuous random variables. Density function. The simultaneous distribution of several random variables. The independence of random variables. The expected value and deviation. Higher momentums. Covariance and the correlation coefficient. Notable discrete and continuous random variables. Characteristic, binomial, Poisson, geometrical, hyper geometrical, steady, exponential, normal distributions. The generating function and the characteristic function. The distribution of sum, product and ratio of random variables. The Student-, Fisher- and Chi square distributions. The conditional distribution and density function. The conditional expected value and its feature. The law of large numbers. Notable inequalities (Markov-, Chebishev-, Kolgomorov inequalities.) Theorems of central limit distributions. Markov chains. The classification of states, the feature of states. Random walk problems. Theory of information. The theory of codes. Entropy. The basic tasks of statistical mathematics. Statistical functions. Point and interval estimators. Hypothesis test. Statistical tests. Fit test. The analysis of regression.

Functional analysis
Credits: 6
Course director: Dr. Barna Garay
Course description: Compactness in complete metric spaces. Normed spaces. Continuous functions, approximation theorems. Fix point theorems. Inverse and implicit function theorems. Lebesgue's measure and integral. Linear operators. Banach-Steinhaus theorem. Fourier series on space of continuous functions. The geometry of Hilbert spaces, complete orthonormal systems, Fourier series. Classical orthogonal function systems. Dual space. Self adjoint operators . Compact operators. The resolvent and the spectrum. Spectral properties of compact and selfadjoint operators. The Laplace operator in Sobolev space.

Linear algebra
Credits: 4
Course director: Dr. Tamás Schmidt
Course description: Complex numbers. The concept of field. Algebra of polynomials. Vector space over the given field, examples for vector spaces. Subspace, linear independence, basis, co-ordinates. Linear projection, matrix, determinant. Transformation of basis, similarity transformation of matrix. The direct sum of vector spaces. Linear projection, its eigenvalue, eigenvector, diagonalability. Jordan's normal form (without proof). Internal product, Cauchy-Schwarz inequality, orthonormal basis, Gram-Schmidt orthogonalisation. Orthogonal polynomials. The selfadjoint, orthogonal and normal projection of Rn and Cn spaces, their diagonalizability in orthonormal basis. Polar decomposition of singular value, bilinear and quadratic forms, congruent transformation of a matrix, theorem of principal axis. Outlook: infinite dimensional normalized vector fields, Hilbert space, Banach space, linear functionals and operators, projective space.

Linear algebra practice
Credits: 2
Course director: Dr. Tamás Schmidt
Course description: In agreement with the course description of the Linear algebra.

Numerical methods
Credits: 5
Course director: Dr. Miklós Horváth
Course description: ynopsis of some generally used calculation in respect of numerical methods. One can face three types of error during any calculation: the first one is due to the fact both model and solution method neglect some aspects of the problem, the second one is the error of used experimental (or any other) data, the third one occurs during calculation because of rounding off. These kind of errors can hardly be eliminated, so every user must face the problem of reliability of the results. Having these in mind the course will deal with the next topics: fitting curves on data ( interpolation), numerical derivation and integration, numerical linear algebra ( iterative solution of equation system, eigenvalue problem), numerical methods of ordinary and partial differential equation (Poisson equation, heat condition, vibrations etc.).

Numerical methods practice
Credits: 2
Course director: Dr. Miklós Horváth
Course description: In agreement with the course description of Numerical methods.

Mathematical methods in Physics
Credits: 4
Course director: Dr. Tamás Keszthelyi
Course description: Vector field, dual field, dual basis. Euclidean space, contra variant and covariant components. Affine point space, euclidean point space, related system. Affine and euclidean tensors. Curvilinear co-ordinates, natural basis. Metric tensor, Christoffel's symbol, covariant derivation. The fundamental of distribution theory, differentials, integration, Fourier transformation and convolution of distributions. The solution of initial value problem, Green functions, prime solution. Dispersion relations, Titchmarsh's theorem. Groups, homomorphysm of groups, subgroups, normal fractional group , factor group, theorem of isomorphism. Presentation of groups, irreducible presentation. Characters, fundamental theorem of orthogonality. Schur lemmas. Continuous groups, Lie algebra, Lie group, and their presentation. SO(3), SU(2).

Mathematical methods in physics practice
Credits: 2
Course director: Dr. Tamás Keszthelyi
Course description: Agree with the course description of Mathematical methods in physics.

Programming (Pascal)
Credits: 4
Course director: Dr. Ferencné Juhász
Course description: The concept of computer software and hardware, the types programming languages. General steps of solving a problem with computer. Elements of PASCAL language, types of data and their operations, Control mechanism and their application. Typical data apparatus and their processing, ordering, searching. Segmentation of programs, data communication. Application of libraries, graphical and mathematical algorithms. The knowledge of tools of modern program innovation and program documentation. Acquiring of knowledge about operation systems and several application programs, MATLAB, electronic mail.

Digital technology
Credits: 4
Course director: Dr. Péter Risztics
Course description: The determination of giving the combination logical network. The logic function, basis of Boole algebra. The table of justice, totally and not totally conditional networks. The most simplest two way realization, building units and applications. The concept of synchronous and asynchronous sequence networks, principle of operation. The determination of sequence networks. The table of states and graph of states. The minimization of sequence networks, methods of state coding. The realization of sequence networks. The control panel, building units, the control functions, output functions. The realization the sequence network with PLA- and memory units. The general layout of computers, the operation of microprocessors, their software model, set of commands. Grouping of computers.

Electronics I.
Credits: 4
Course director: Dr. Géza Kolumbán
Course description: Definitions, circuit elements and Kirchhoff's rules. Computer technique: relative and logarithmic units. Branch point potentials- and mesh current methods, the most important theorems for linear networks. Some types of signal processing networks, the concept of ideal diode and amplifying. The approximation with Fourier series. The transient response: the concept of impedance, the complex range of frequencies. The stationary solution: one particular solution of inhomogenous differential equation. The concept of complex voltage and current. The complex exponentials as eigenfunctions. The complex frequency range. The total response of linear networks: the general solution of differential equation and its physical meaning. Steady state condition of sinusoidal excited networks, the determination of transmission function in frequency range. The concept of resonance. The realization of filters. Analysis of networks, the concept of one gate and two gate. The determination of impedance matrix and application, the Bode diagram. Connection of quadripoles, block diagrams, the concept of feed-back. The analysis of non linear networks, the determination of short time models, the concept of distortion. The use of non linear characteristics: rectification, mixing and frequency multiplying.

Electronics II.
Credits: 2
Course director: Dr. Géza Kolumbán
Course description: The operation of mostly used electronic parts, analysis of characteristics, appliance modelling. The analysis of analogue circuit which contains discrete elements: the analysis of circuit containing diodes, bipolar- and FET transistors. Plan of transistor amplifier: the determination of working point and the plan of signal way. The analysis of multi-stage amplifier. The concept of feed-back, the stability of negatively feed backed amplifiers. The layout and application of operation amplifiers. The most important parameters of real operation amplifier. Working connections of diodes and transistors, the Ebers' model, the determination of condition of devices. The main features digital circuits. The operation of the TTL, the TTL-LS, the ECL and the CMOS circuits and survey of most important features. Examinations of some complex electrical circuits: A/D and D/A converters, sampling holding circuits, oscillators, modulators and demodulators.

Electronics laboratory practice I.
Credits: 2
Course director: Dr. Barna Szepessy
Course description: The aim of the laboratory is introducing to basic knowledge of methods of electrical measurements: to get the master of basic practice in design of experiments, design of measurement equipment, estimation of components of uncertainty of measurement, setting up the uncertainty/error budget, exception of importance of trace ability and track ability. Laboratory measurements: Introduction laboratory. The use of instrument HAMEG. The measurement of input resistance and the upper and lower limit frequencies of instruments. The measurement of band-width and mid-range. The measurements of basic digital circuits.

Electronics laboratory practice II.
Credits: 2
Course director: Dr. Barna Szepessy
Course description: . In this semester we will examine the next problems of method of measurement (especially connected with 20 related item of ISO 9001): the control of technical design, the treatment of documents and data, controlling and examination, the controlling/verifying of devices of controlling, measuring, examining, the treatment of non suitable part, statistical methods to analysing measurement data. Laboratory measurements: Introduction measurement. Measurement of offset current and voltage of operation amplifier. The measurement of dynamic features of operation amplifier. Frequency compensation of amplifiers:  pole zero cancellation etc. Miller effect. Bootstrapping.

Methods of measurements
Credits: 2
Course director: Dr. Béla Pataki
Course description: Modelling in methods of measurements. Grouping signals. Deterministical signals and their description. Stochastic signals and the tools of mathematical determinations. The basic problems of digital signal processing: sampling, interpolation. The basis of DFT and digital filtering. The types of A/D and D/A converters and their features. he concept of systematic and incidental error. The determination of the result of measurement. The measurement time free parameters of signals: measurement of peak- and effective value, the average value measurement. The devices of measuring current and voltage. The devices of measuring time and frequencies. The measurement of signals: analogue- and digital oscilloscopes. The devices of measuring impedance. The device of spectrum analysis.

Chemistry I.
Credits: 3
Course director: Dr. Attila Bóta
Course description: Chapters in general and inorganic chemistry, in physic chemistry, in Colloids and in technical chemistry, and relationship between them. The stoichiometrical basic of chemistry calculations. The description of gas, liquid and crystalline states, emphasizing the reactions in water solutions. The energetic and time dependent chemical processes. The structure of atom and molecule. The physicochemical reactions at phase boundary surface. Features of adsorbents. The characteristic properties of chemically separated material systems. Features and qualification of important energy carriers.

Chemistry II.
Credits: 4
Course director: Dr. Attila Bóta
Course description: Chapters of special boundary areas of chemistry. Water chemistry: the most important properties of water. Colloids: qualification of adsorbents. New materials: fullerens and crystal liquids. Biophysical chemistry: liotrop systems. There are laboratory practice connected with this course, the topics are: Detection of cations and anions, examination of quality of water, Potentiometric titration, determination of mass of molecule Examinations with spectroscope, Examination of galvanic element, Examination of liquid/gas boundary layer, Examinations of Colloid structures with small angle X-ray investigations.

Experimental physics I.
Credits: 4
Course director: Dr. András Tóth
Course description: Kinematics of point particle. Newton laws. Galileo transformation, the principle of relativity. Accelerating co-ordinate systems. Work, energy, conservation of energy for point particle. Motion of body, theorem of centre of mass. Conservation laws in point systems. Rotation of a rigid body about a fixed axis, gyroscope, the complex motion of rigid body. Electric field, the fundamental laws of electrostatic fields. Dielectrics. Energy of electric field. Time stable electric current, electric conduction, contact effects. Magnetic field, magnetic induction. Forces in magnetic fields. The fundamental laws of permanent magnetic field. Magnetic field in substance. Changing magnetic field, the induction law, self inductance, mutual induction, the energy of magnetic field. Movement induction. Changing electric field, displacement current. The integral forms of Maxwell's equations.

Experimental physics II.
Credits: 4
Course director: Dr. András Tóth
Course description: Oscillatory motions, harmonic, damped and forced oscillations. The energy of harmonic oscillation, coupled oscillations. Propagation of waves, one dimensional harmonic wave. Dispersion, group velocity. Waves in two- and three dimension. Elastic and electromagnetic waves, the one dimensional wave equation. Propagation of energy in wave. Interaction of electromagnetic wave with substance. Thermal radiation. The Doppler effect. Huygens' principle, reflection and refraction of waves. Polarization of light. The propagation of electromagnetic wave in anisotropy medium. Interference. Standing waves. Aberration of waves. Quantum properties of electromagnetic field and the wave-like behaviour of particles. Atomic spectra, atomic energy levels, Bohr's model. The fundamental of wave mechanics. Particle wave duality, wave function. The Schrödinger's equation and its solution in simple cases. Induced emission, the operation of laser.

Experimental physics III.
Credits: 4
Course director: Dr. András Tóth
Course description: Elastic deformations of solids. The fundamentals of hydrostatics and hydrodynamics. The temperature, equation of state of ideal gas. Kinetic gas theory. Real gases. Transport phenomena in gases. Describing the thermodynamic state of the system. Heat, internal energy, the first law of thermodynamics. State changes of ideal gas, cycles. The second law of thermodynamics, the entropy. The statistical meaning of entropy. Some properties of homogeneous systems. Criteria for equilibrium, thermodynamic potentials. Differential relationships: state equations, Maxwell's relation, Gibbs-Helmholtz equations. Chemical affinity, the third law of thermodynamics. Changing amount of stock, chemical potential, Euler's equations, Gibbs-Duhem relation. Phase transitions in one component systems, the Clausius-Clapeyron equation. More component systems: dilute solutions, chemical reactions, the mass action law.

Experimental physics practice I.
Credits: 2
Course director: Dr. András Tóth
Course description: Problem solution of course Experimental physics I.

Experimental physics practice II.
Credits: 2
Course director: Dr. András Tóth
Course description: Problem solution of course Experimental physics II.

Environmental and radiation protection
Credits: 4
Course director: Dr. Péter Zagyvai
Course description: The feature of radioactive decompositions, the interactions between nuclear radiation and substances medium. Fundamentals of dosimetry and radiation protection. Simple models of dosage calculation. The biological effects of ionizing radiations. The interpretation of risk, connection with first principles of radiation protection. Authority norms of radiation protection. The radiation protection importance of natural radioactive isotopes. Sources of artificial radioactive contamination. The measurement methods and devices of dosimetry and radiation protection radioanalytics.
The aim and tools of environment protection. Exhausting and reviving natural resources. Interactions between the generation of energy, the industry and environments. The structure and composition of atmosphere. Air fouling materials. Methods of measurement of emission and immission. Air-fouling at work site and at home. Characteristics and qualifications of water sets. The water fouling organic and inorganic materials. Investigation of quality of water. Treatment technologies of drink and slop water. Utilization of wastage, destroying them. Soil pollutions, soil unpollution processes. Treatment of dangerous waste. Methods of measurements of risk.

Experimental nuclear physics
Credits: 3
Course director: Dr. Zoltán Szatmáry
Course description: Properties of stable nucleons and nuclear forces. The structure of atomic nucleus and its properties. The properties of nucleons. Nuclear forces. The stability of atomic nucleus, defect of mass, bonding energy. The liquid drop model and the formula of semi-empirical bonding energy. The possibilities of release of nucleon energy. Radioactive decay of atomic nucleons. Radioactivity: the types of radioactive decays and characteristic quantities. The time dependence laws of radioactive decay: simple decay, complex decay, decay series. Alpha-, Beta-, Gamma decay. Nuclear reactions. The general laws and types of nuclear reactions; mechanism of nuclear reactions (direct nuclear reactions and complex nucleons). Cross section (microscopic and macroscopic). The types and characteristics of neutron nuclear reactions. The energy dependence of cross section of neutron nuclear reactions. The fundamentals of neutron deceleration. Quick neutrons, resonance neutrons, thermal neutrons. Interaction of radioactive radiation and the substance. Interaction between charged particles (alpha-, beta- radiation), neutron- and gamma radiation and substance; decrement of radiation passing through the substance. The main characteristics of nuclear detectors: gas ionizing detector, scintillation register, semiconductor detector, thermoluminescent detector, solid state trace detectors. Neutron detectors. Fission. The mechanism of fission. Fissures, the properties of fission neutrons. Releasing energy of fission, and its time and space distribution. Chain reaction, the criteria of self supporting chain reaction, the multiplying factor. The principle layout of thermal atomic reactors. Nuclear reactions producing fissionable isotopes. The main types of nuclear accelerating devices.

Mechanics
Credits: 4
Course director: Dr. Tamás Keszthelyi
Course description: Reference system, Newton's axioms, inertial system, motion in accelerating system, inertial forces. Motion in one dimension, in a central field. Two body problem, planetary motion, scattering of particles. Equations of motion of a system of particles, and their integrals. Motion of rigid body, Euler's equations. Principle of virtual work, d'Alembert's principle. Constraints, Lagrange's equations. Hamilton's principle. Canonical equations, canonical transformations, Hamilton-Jacobi equation. Symmetries, Noether's theorem, constants of the motion. Poisson brackets. Mechanics of deform able bodies, equilibrium, elastic waves. Continuous systems Hamilton's principle. Equation of motion of relativistic particle, Lagrange's function, Hamilton's function. The relativistic Hamilton-Jacobi equation.

Mechanics practice
Credits: 2
Course director: Dr. Tamás Keszthelyi
Course description: Agree with the course description of Mechanics.

Hydrodynamics
Credits: 3
Course director: Dr. Ferenc Szlivka
Course description: Ideal fluids: equation of continuity, hydrostatics. Euler's equation, theorems of vortex,  Bernoulli's equation. Viscous fluids: theorem of impulse, equation of energy. Stress tensor, equation of motion, Navier-Stokes's equation. The law of similarity, similarity numbers. The turbulence effect, its description. The basic equations of dynamics of gases, numerical solution of one dimensional tube flow. Shock waves.

Electrodynamics and theory of relativity
Credits: 4
Course director: Dr. Pál Pacher
Course description: Maxwell's equations. Green's theorem, the Green function, Neumann and Dirichlet boundary conditions. Poisson and Laplace equations. Dipole, multipole expansion. Surface charge, dielectric. The equations of electrostatics in dielectric media. The vector of polarization, surface and volume charges of polarization. The electric displacement vector. Stationary currents. Magnetic dipole. Magnetization, magnetic field. The vector potential. Magnetic scalar potential. Quasistationar processes, Faraday's law of induction. Quickly time varying electromagnetic fields. Electromagnetic potentials, Gauge invariance Lorentz gauge and Coulomb gauge. Retarded potentials. Lienard-Wiechert potentials. Radiation of accelerating charge. Wave guides, Resonant cavities. The basic equations of electrodynamics with 4-vector symbols. The field strength tensor. The energy momentum tensor.

Electrodynamics and theory of relativity practice
Credits: 2
Course director: Dr. Pál Pacher
Course description: Complement chapters of the course of Electrodynamics and relativity theory, demonstration of applied solution methods in electrodynamics with the help of problems.

Quantum mechanics
Credits: 5
Course director: Dr. Barnabás Apagyi
Course description: The limits of classical physics. Wave mechanics. The mathematical and physical fundamentals of quantum mechanics. Operators representing physical quantities. Bonded states. Scattering states. Motion in electromagnetic field. Relativistic quantum mechanics and symmetries.

Quantum mechanics practice
Credits: 2
Course director: Dr. Barnabás Apagyi
Course description: In respect of course Quantum mechanics solution of special problems. Typical problems: Compton scattering, Bohr-Sommerfeld quantum condition, one dimensional Schrödinger's equation, Method of Sommerfeld polynomials, The harmonic oscillator, The spectra of momentum, The solution of Schrödinger's equation in central potential, H-atom, The sum of momentum operators, Clebsch-Gordon coefficients, method of partial waves, Born approximation, Time dependent and time independent perturbation theory, Fermi's golden rule, Pauli equation, solution of Dirac equation: free electron, rectangular potential gate, central potential.

Statistical physics
Credits: 5
Course director: Dr. János Kertész
Course description: Introduction, time scales, equilibrium, partial equilibrium, detailed equilibrium, equilibrium distributions, ergodicity and irreversibility. The fundamentals of statistical physics, Liouville theorem and equation, density matrix and Neumann's equation, normal systems, ensembles, the fundamentals of thermodynamics, fluctuations.  Ideal gas, Ideal Fermi-gas, properties at low temperature, ideal Bose-gas, Bose-Einstein condensation, thermal radiation, the classical limit. Quasi particles, phonons, superfluidity, the fundamentals of the Fermi-liquid. Screening, virial expansion, states, phase transitions, mean field theories, scaling, the renormalization group, Monte-Carlo   method.  Time dependent processes, Wiener-Hincsin theorem, linear transport and cross effects, linear response theory, Brown motion, Langevin equation, Fokker-Planck equation, master equation, H-theorem, Boltzmann equation, irreversibility.

Statistical physics practice
Credits: 2
Course director: Dr. János Kertész
Course description: Thermodynamics, the basic concepts of statistical physics, the descriptions of microscopic states, Liouville theorem. Gibbs ensembles, micro canonical ensemble, the criteria of equilibrium, entropy, canonical ensemble, free energy, theorem of equipartition, grand canonical ensemble and the chemical potential, T-p ensemble, Gibbs potential, fluctuations. Ideal quantum gases, Fermi and Bose statistics. Classical limit, spin susceptibility of Fermi gas, Bose condensation. Systems with interaction, virial coefficients, Van der Waals gas. The programme of practice and lecture are in close connection.

Solid state physics I.
Credits: 2
Course director: Dr. Alfréd Zawadowski
Course description: Crystal lattice, lattice vector, translational symmetry, reciprocal lattice, crystal symmetry, crystal lattices. Diffraction by a crystal lattice: conditions of diffraction. Lattice vibrations: classical theory of vibrations of one dimensional and three dimensional chain. Quantization of vibrations, phonons. Measurement of phonons and light scattering. Electrons in crystal lattice: Bloch's theorem, band structure, density of states, Wannier's functions. Electron occupying, Fermi surface, Sommerfeld expansion, electron specific heat and susceptibility. Fundamental theory of electron transport. Drude model, Hall effect. Semiconducting materials. Donors and acceptors. Distribution of electrons. Transport in semiconductors: mobility, semiconductor diode. The effect of transistor.

Solid state physics II.
Credits: 5
Course director: Dr. Alfréd Zawadowski
Course description: The second semester is special foundation teaching of solid state physics. This semester is in close connection with first semester. The next topics will be outlined (in respect of basic knowledge of first semester): formal transport theory, electron phonon interaction and interaction of electrons with impurities, properties of semiconductors, electron electron interaction, fundamentals of magnetism, features of superconductors.

Solid state physics practice
Credits: 2
Course director: Dr. Alfréd Zawadowski
Course description: Problem solution practice to acquire the subject of the first semester of the special basic course of solid state physics. The students will do concrete calculations in next topics: crystal lattice, reciprocal lattice, X-ray scattering; dynamics of lattice vibrations, specific heat of phonon; electron band structure and Fermi surface in weak periodic and tight-binding potentials; electron specific heat and density of state.

Nuclear and particle physics I.
Credits: 4
Course director: Dr. Csaba Sükösd
Course description: Review of measurable data of ground state nucleuses. The structure and energy of nucleus, conditions of stability. The radius of nucleus. The impulse momentum and the statistics. Electromagnetic momentums. Models of nucleus. The saturation of bonding energy and the Fermi-gas model. The shell model of nucleus, basic theory, experimental prooves and conclusions. The fundamental of collective model, the dynamics of nucleus-core. The matter of nucleus. Interaction forces between nucleus. The deuteron. The meson theory of nucleus forces. Two nucleon potentials. Charge independence and isospin. Mirror nucleus. Isobar analogue states. Charge multipletts. Excited states of nucleus. Yrast states, high spin states, giant resonances. Hyper and super deformed nucleus. The theoretical description of nucleus decay. Electromagnetic transitions in nucleus, the * decay. Multipole transitions and the Weisskopf's estimation. Selection rules. The weak interactions of nucleus, the description of * decay. Fermi and Gamow-Teller transitions. The reason of *-decay. The nucleus fission. The discussion of nucleus reactions. Elements. Scattering theory, partial waves, S-matrix and T-matrix. Direct reactions.  DWBA, method of coupled channels. Resonances, intermediate nucleus and optical model. Statistical decays, the formalism of Hauser-Feshbach. The treatment of complex particles, heavy ion reactions. Nuclear astrophysics. The fusion. The energy production of stars, the development of elements and the nuclear star development.

Nuclear and particle physics II.
Credits: 4
Course director: Dr. Péter Kálmán
Course description: Klein-Gordon and the Dirac equation. The Lorentz covariance of Dirac equation, free and bonded solutions. The negative energy solutions and the positron. Conjugation of charge, time reversibility and other symmetries. The classical space theory and the canonical formalism of quantum space theory. The quantization of free electromagnetic field. Quantization and spin. The zero point energy of electromagnetic field, the vacuum fluctuation and its conclusion. Not electromagnetic interactions. The hard interaction and the hadrons. The quark model and primitive quark closing. The weak interaction and leptons. The principle problems of interacting fields. Mass and charge renormalization in quantum electrodynamics.

Optics I.
Credits: 4
Course director: Dr. Péter Richter
Course description: Light and substance interaction (phenomenological description, complex refractivity, dispersion, anisotropy, optical rotation). The feature of electromagnetic wave at plane boundaries. Fresnel's formulas. Interference, one beam and multiple beam interferometers. Diffraction, (Fresnel, Fraunhofer), holography. Coherence, temporal coherence, spatial coherence. Optical projection, resolving power of optical systems. Wave guide optics, integrated optics, optical fibre. Light and substance interaction (microscopical description, semi-classical and quantum mechanical bases). Polarization, crystal optical, electro-optical, magneto optical effects. Quantum optical effects, lasers. Non linear optical effects. Scattering deviations, spectroscopy.

Atomic and molecular physics
Credits: 3
Course director: Dr. István László
Course description: Quantum mechanics of many particles system. General principles. Some Hamilton operator of simple, many particles systems. Required application of approximation methods. Spin orbitals. The Pauli's principle. The Born-Oppenheimer approximation. The determinant forms of wave functions. The variational principle. The independent particle approximation. The Hartree-Fock method (without any condition). Koopman's theorems. The properties of solution of Hartree-Fock equation. The Hartree-Fock method in the case of closed shell systems. The Hartree-Fock method in the case of open shell systems. The Roothaan's equations. The separation of motion of central mass. Electronic structures of atoms. Electronic states of atoms. The electronic structure of multielectron atoms. The group theory and the symmetries of wave function. The density matrix. The virial theorem and the Hellmann-Feynman theorem. Electronic structures of molecules. Outline, selected chapters.

Laboratory in physics I.
Credits: 3
Course director: Dr. László Vannay László
Course description: Introduction and theoretical representation. Basic measurement of electronic DC current. The determination of friction coefficients. Investigations with oscilloscope. The determination of velocity of sound on air. The calibration of heat sensing device. The examination of semiconductor thermoelement. The examination of semiconductor heat pump (Peltier-element). The measurement of resistance, inductivity and capacity, the examination of oscillating circuit and filters. The examination of semiconductor circuit elements. The examinations of basic circuits of semiconductor electronics. The measurement of displacement with inductive measurement converter. Measurements with strain gauge.

Laboratory in physics II.
Credits: 4
Course director: Dr. László Vannay
Course description: The measurement of Young's modulus with static method. The examination of forced oscillation and resonance. The examination of standing waves in elastic string. The determination of coefficient thermal expansion of solid materials. The examination of free surface of liquid. The measurement of surface tension of liquids I.-II. The measurement of flow velocity of liquids. The measurement of viscosity of liquids. The measurement of water content of air. The determination of specific heat of solid matters. The examination of heat conduction. The measurement of heat transfer coefficient. The examination of thermal radiation. Refraction and reflection of light, the measurement of refractive index of solids and liquids. Examinations of optical lens. Examinations with optical microscope.

Laboratory in physics III.
Credits: 4
Course director: Dr. László Vannay
Course description: Microwave optics. The measurement of specific charge of electrons (e/m). The determination of Boltzmann constant (e/k). The measurement of the ratio of Planck and Boltzmann constant (h/k). The measurement of magnetic resistance, the gap, the Hall-effect in semiconductor. The measurement of photo effect (h/e). The Franck-Hertz experiment. The examination of acousto optical diffraction of light. The optical heterodyne detection and its application. The examinations of lens errors with tracking beam method. The measurement of absorption of Gamma radiation, measurement of density. The examination of absorption and reflection of beta radiation, the measurement of thickness. The examination of spectral properties of light sources and light sensors.

Laboratory in physics IV.
Credits: 4
Course director: Dr. László Vannay
Course description: The laboratory measurements mainly gives know ledges in material sciences and there will be some measurements of experimental nuclear physics. The students will measure the electro-optical, non-linear optical, magneto optical, piesoelectronical, piroelectronical and etc. properties of matters, they will face their measurement methods. There will be also thin layer physics, surface examination (for example STM) measurements and some fundamental measurements in nuclear physics .

Laboratory in physics V.
Credits: 4
Course director: Dr. Imre Péczeli
Course description: The examination of semiconductor optical detectors. Surface analysis with Auger- spectroscope. X-ray diffraction. The examinations of layer structures with SIMS method. The determination of parameters of laser beam. The electronic granule screen interferometer. Holograms. Making holographic interferogram. The measurement of 1/r2 function of radiation source. The examination of isotopes with scintillation detector. The Gamma spectroscopy with semiconductor detector. The working of neutron detector. The determination of thermal flux of neutrons. The measurement of activity with beta, gamma coincidence method.

Economics
Credits: 2
Course director: Dr. Edit Romvári
Course description: The fundamentals of economy, processes and analytic implements. Market, mechanism of market. The elements, structure of market, types of markets. The analysis of demand and supply, functions of demand and supply. Adaptability of demand and supply. The basic rule of consumer's decision. Disinterest curve and consumer equilibrium. Venture, company: optimal input consumption, profit maximization output decision. Costs and profits, closing down, cover and extent economicalness. Financing of venture. The role of state in market economy: activity in organizing the economy, market influencing.

Industrial management and business economy
Credits: 2
Course director: Dr. János Kövesi
Course description: The concept of management, main trends, special fields. Business economics I.: costing. Enterprise economics II.: investments calculation of refunds. Product development I.: product life curve, simultaneous (concurrent) design. Product development II.: double propelled product development. Team work I.: the concept, types, formation phases of the team. Team work II.: the composition of the team, team roles. Team work III.: techniques of mental works of groups. Project management I.: the concept of the project, life cycle, condition of function. Project management II.: net design. Technological management I.: technological life cycles. Technological management II.: technological strategies. Quality management II.: quality reliability, quality controlling. Quality management II.: Quality insurance, TQM.
 

 

Compulsory Facultative Professional Courses
(they are not module courses)   

Photonical devices
Credits: 4
Course director: Dr. Imre Mojzes
Course description: Physical and technological basics, optical data transmission and signal analysis, passive and active elements. Light sources and sensors: with non coherent (filament lamp, luminescent elements, photo conductors, LED, PD, PT, solar cells) and with coherent light processing devices (solid state lasers, laser diodes, super lattices). The properties and materials of passive elements: glasses, crystals, polymers. The properties and materials of active elements: modulators, deflectors, polarizators, filters, frequency converters, bistable elements, switches, solitons in data transmission, liquid crystal devices. Light sensitive materials and optical memory: the parameters of data recording, systems based on silverhalogenid, silver free materials, magneto optics. Optical data transmissional and data processing systems: light fibre optics and data transmission, picture processing, optical sensors.

Optics II.
Credits: 5
Course director: Dr. Gábor Szarvas
Course description: Macroscopical Maxwell's equations and optical wave propagation. Scalar- diffraction:  Helmholtz's equation and integral formulas. Consequences of integral formulas: spectra with plane waves, paraxial wave equation, the equivalence of the paraxial wave equation the Fresnel's approximation. Gauss beams. Geometrical optics. Fermat's principle, Schnell's law, examples for stigmatic, aplanatic and absolute projection. Gauss' optics. The law of lens. Geometrical aberrations, wave and beam aberrances, design of lens. Temporal and spatial coherence. The projection of coherent object by wave optics. The Abbe's description. The projection of incoherent object, defects of aberrations, OTF, MTF. Crystal optics. The fracture of extra ordinal beams, conical refraction, Huygens- Fresnel principle for extraordinary waves. Optical wave guide.

Macromolecules
Credits: 2
Course director: Dr. Miklós Zrínyi
Course description: The chemical structure of macromolecules. Interactions in ideal and real macromolecules. Polymer systems: polymer solution, polymer gels, physical chemical properties of polymers. The statistical description of molecule chain deformation. Critical phenomena in polymer systems. Clew globule transition. Polymers commensurability. Elastic and viscous properties.

Nonlinear oscillations
Credits: 2
Course director: Dr. Gábor Stépán
Course description: he basic concept of stability theory: Equilibrium of mechanical systems, Ljapunov's stability. The stability in conservative systems, theorems of Ljapunov. The basic concept of catastrophe theory. Linear limit of stability. Examples in mechanics. The concepts of nonlinear oscillations: systems of one degree of freedom, phase plane method. Typical nonlinear machine units in swinging systems. Nonlinear oscillations of conservative systems. The estimation of period of oscillation. Chaos in conservative systems. Oscillations around equilibrium state stabilized by gyroscope, the application of KAM theory. The many body problem. Construction of trajectories in attenuated system. Liénard's and Bendixson's criteria of exist of boundary cycle. The Hopf's bifurcation method and the use of central ensemble for determination of periodical motions. Examples in mechanics: the fitful motion, oscillation of instrument machine, robots, vibrating problems of machine wheel, its chaotical motion. The calculation of chaos and recognizing it from measurements. The turbulence in dynamical systems. Bifurcation effects in hydrodynamics, the laminar turbulent transition, connection between chaos and turbulence. The stability of parametrically excited mechanical systems. The period reduplicative bifurcation. Non linearly excited oscillations, resonance curves, magnification diagrams in nonlinear systems. Nonlinear oscillations and chaos in discrete systems. The dynamics of machines controlled by computers. Micro chaotical oscillations around the digitally stabilized equilibrium of mechanical systems.

Quantum mechanics II.
Credits: 2
Course director: Dr. Péter Kálmán
Course description: Diary's formulation of Quantum mechanics. Canonical quantization. The algebraical solution of harmonic oscillator. The coherent state and its properties. Time developing operator. Schrödinger's, Heisenberg's and interaction picture. Time dependent perturbation theory. transition probability. Gauge invariance in Quantum mechanics. The elements of relativistic Quantum mechanics.

Selected chapters in Quantum mechanics
Credits: 2
Course director: Dr. Barnabás Apagyi
Course description: Theory of measurement. Direct scattering theory. Inverse scattering theory. Algebraical methods. Fractional statistics. Geometrical phase factors.

Technical use of computers
Credits: 3
Course director: Dr. László Füstöss
Course description: The aspects of choices of suitable computer system. Operation systems. Measurement controlling and data processing. Computer simulation. Network know ledges. Electronic mail. Computer image procession and form identification. The use of CAD systems: concept of constructions; technical representation; help of computer in projects.
 
 

 

Compulsory Facultative Courses  

Taxation, accounting, social insurance
Credits: 2
Course director: Dr. Gábor Szabados
Course description: Foundation of undertaking, the basics of book-keeping by double entry and by one entry, types of taxes, taxes burdening undertakings, tax counting, immunity from taxes, discounts. Social insurance rights burdening different types of activities, engagement of defrayment. Insurance opportunities of decreasing of risk of undertakings.

Management for engineers
Credits: 2
Course director: Dr. János Kövesi
Course description: Basic concepts, management tendencies. Personal efficiency. Work in groups. Leader in corporation. Communication. Innovative management. Value analysis, development of product. Production management, quality management, management of resources. Project management. Information management. The decision.

Technical reliability of production systems, quality regulation
Credits: 2
Course director: Dr. János Kövesi
Course description: The basic of quality regulation. Quality schools (japanese, west-european, american). The strategic system and management of quality trend. The pyramid model of realization of quality model of Hungary, the tactical management system of quality trend, the specialities of model leading in Hungary. The economy of quality, quality and reliability. The tactical and operative management of quality design. The place of quality control and its operative methods in quality management, definition of reliability, components of reliability. Mathematical modelling. The reliability function. Reliability parameters. Markov processes in system analysis. The reservation. The strategies of maintenance. The system establishment by minimal cost principle or by maximal assurance principle. The lifetime optimization. Inquest methods. CARM.

Managing technological changes
Credits: 2
Course director: Dr. Béla Pataki
Course description: The concept of change management, its process. The role of technological strategy, the opportunity of technology change. Innovative and technological transfer. The plan of change. Force space analysis, winning the key members. The implementation of new technology, confirm the change. The use of project management application during realization. Technology change and culture of corporation, technology change and corporation structure.

Ergonomy
Credits: 2
Course director: Dr. Miklós Antalovits
Course description: The development of subject and concept of ergonomy. The concept of human engineering and its application opportunities in engineering practice. The role of ergonomy in leadership activity. The optimization of human machine environment systems: principles, models, methods, instance studies. The design and qualification of working place and working environment by ergonomical aspects. The burden and employment. The ergonomy in market economy. The exploration of customer claim to product and its forcement during product developing. The ergonomy outside work: at home, in transport, in school, in free time activity, etc. The characteristics of human information processing, the concept of cognitive psychology. The basic problems of software ergonomy: the user interface, the quality of dialogue, ergonomical design and qualification softwares. The human factors in process trends. The methods of determination and increase of human reliability. The stress and he human error. The opportunities and methods of prevention of bad consequences. The effect information technologies on work, on work corporations and on work conditions. The human factors of development and introduction of computer managed technologies.

General technical language (English, German, French, Russian)
Credits: 2
Course director: Dr. Zoltán Sturcz
Course description: Establishment of basic skills in technical communication for successful manifestation in written and oral trade. The content of context is general technical language like. The treatment of grammar is determined by communication functions. The oral and written tasks are based on presentation, reproduction, problem solving situation of real problems in every case. During the semester we will cultivate the next skills: reading skill in technical text, comprehension after hearing, readiness of speech.

Special know ledges of technical language (English, German, French, Russian)
Credits: 2
Course director: dr. Zsuzsa Gombos Sziklainé
Course description: Attaining specific vocabulary of technical language starting from basic features of technical communication, and by terminology attaining the language forms connected with different communication situation. The oral and written skills embrace the knowledge of drafting of different language functions and their productive use.

Engineering ethics
Credits: 2
Course director: Dr. László Molnár
Course description: From job to occupation. The engineering occupation and traditional occupations. Roles of engineers, and conflicts connected with this role. The engineer as a manager. The engineer as a employed. The engineer as a official. The engineer as an enterprising. The role of engineer societies and codex of ethics. The ethics of technological civilization. The main questions of ethics of business life. Problems of environmental ethics. Main types of moral theories. The utilitarian ethics. The deontological ethics. Virtuous ethics. The judgement of business in traditional society and in ethics. The protestant ethics and mentality of capitalism. (Occupation, diligence, temperance) The concept of the selfishness, profit and public good in ethics: their functions in business life. Liberal ambitions to reconcile the making profit and human dignity. The stabilization of peaceful enterprise forms. The confidence and the business. Concealment, secret, deception, lie versus fidelity, honesty, justness, fairness. The ethics of market behaviour. Advertising, pricing, competition. The society responsibility of enterprising and managers.

Technical law
Credits: 2
Course director: Dr. László Kleeberg
Course description: The basic concepts of political science and jurisprudence, the constitution public administration. The representation of civil law, civil procedure law and firm law, especially technical law relations to of contracts, enterprise forms, economical societies. Industrial law protection, laws of mental compositions - invention, know-how, industrial sample - software data protection. Writing of documents and petitions. Technical questions of right of labour, environment law, criminal law, private international law. Problems of trade specific technical laws.

Environment economy
Credits: 2
Course director: Dr. János Szlávik
Course description: The interpretation of production opportunities connected with environment (the statical and dynamical interpretation of TL curves; maintainable development). The basic relations of economy of natural energy source. The problem of measurement, the distortion character of economical indexes (GDP; GNP), tries to get more reliable measurements (NEW, ISEW). The limit and opportunities of market in environment economy (ivil goods and public goods; extrenals). The economical basis of environment controlling. Applications of farm equipments in OECD counties in environment controlling, their opportunities and ways of introduction in Hungary. Analysis of environment risk. The economical relations between environmental influence examination.

Chapters in history of physics
Credits: 2
Course director: Dr. Gábor Biró
Course description: Introduction: historical scheme about connection of physics and techniques. The basis Galileo Newton dynamics. From the theory of caloric to supposition of heat motion. The critics of newtonian force description by electromagnetics. The prehistory of relativity theory. The accumulation of experimental facts destroying classical physics - preparation of quantum theory. Experimental facts, the relation of mathematical description and physical theory.