Compulsory CoursesSHORT COURSE DESCRIPTIONS OF ENGINEERING PHYSICS
Compulsory Facultative Professional Courses
(they are not module courses)
Compulsory Facultative 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.
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.
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.