course 
code 
teacher 
ws 
ss 
ws cr. 
ss cr. 
Compulsory courses 
Calculus A3  01MAA34 
Vrána 
4+4 z,zk 
4+4 z,zk 
10 
10 
Course:  Calculus A3  01MAA3  Ing. Fučík Radek Ph.D. / Ing. Vrána Leopold  4+4 Z,ZK    10    Abstract:  Function sequences and series, foundation of topology, and differential calculus of several variables.  Outline:  Function sequences and series: Pointwise and uniform convergence, interchange rules for limits, derivatives and integrals. Fourier's series, expansion of a function into trigonometrical series, tests for pointwise and uniform convergence of trigonometrical series, completeness of trigonometric system. Topology of normed linear space, compact, connected and complete sets, fixpoint theorem. Differential calculus of several variables: directional derivatives, partial and total derivatives, meanvalue theorems, extremum, manifolds, constrained extrema.  Outline (exercises):  Uniform convergence. Interchange rules. Expansion of a function into trigonometrical series.
Directional derivative. Total derivative. Local extrema.
 Goals:  To acquaint the students with the properties of function sequences and series, expansion of a function into trigonometrical series, with an introduction to the topology, and with foundation of differential calculus of several variables.  Requirements:  Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA2, 01LA1, 01LAA2 held at the FNSP CTU in Prague).
 Key words:  Function sequences and series, Fourier's series, topological and metric space, compactness, connectness, completeness, total derivative, local extrema.
 References  Key reference: W.H.Fleming,Functions of Several Variables, AddisonWesley, Reading, MA, 1966.
Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis  An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009

Course:  Calculus A4  01MAA4  Ing. Vrána Leopold    4+4 Z,ZK    10  Abstract:  Integration of functions of several variables, measure theory, foundation of differential and integral calculus on manifolds and complex analysis.
 Outline:  Lebesgue integral: Daniel?s construct, interchange rules, measurable sets and measurable functions. Fubini's theorem, theorem on changing variables. Parametrical integrals: Interchange theorems, Gamma and Beta functions. Differential forms: conservative, exact and closed form and their relations, potential. Line and surface integral: Green's, Gauss' and Stokes' theorem. Complex analysis: analytic functions, Cauchy's theorem, Taylor's expansion, Laurent's expansion, singularities, residue theorem.  Outline (exercises):  Smooth manifolds. Constrained extrems. Differential forms. Lebesgue integral in several variables. Use of Fubini's theorem and theorem on changing variables. Use of Gamma and Beta functions for computation of integrals. Computation of integrals
 Goals:  To acquaint the students with foundations of Lebesgue integration and with foundations of complex analysis and its use in applications.  Requirements:  Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA23, 01LA1, 01LAA2 held at the FNSP CTU in Prague).  Key words:  Lebesgue integral, measurable functions and sets, Gamma and Beta functions, line and surface integral, divergence theorem, Cauchy's theorem, residue theorem.  References  Key reference: W.H.Fleming,Functions of Several Variables, AddisonWesley, Reading, MA, 1966.
Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis  An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009


Numerical Mathematics 1  01NUM1 
Oberhuber 
3+1 z,zk 
  
4 
 
Course:  Numerical Mathematics 1  01NUM1  Ing. Oberhuber Tomáš Ph.D.  3+1 Z,ZK    4    Abstract:  The course introduces to numerical methods for solving the basic problems arising from technical and research problems. The accent is put on a good understanding of the root of theoretical methods.  Outline:  1. Recapitulation of necessary concepts from linear algebra and functional analysis.
2. Direct and iterative methods for solving linear algebraic equations. Matrix inversion.
3. Solving the partial eigenvalue problem.
4. Solution of the full eigenvalue problem.
5. Solving the equation f (x) = 0
6. Systems of nonlinear algebraic and transcendental equations.
7. Interpolation functions by polynomials.
8. Numerical calculation of derivatives.
9. Numerical calculation of integral
 Outline (exercises):  1. Practicing rules of operations with triangular matrices, proofs of theorems on decompositions of square matrices, derivation of decomposition formulae.
2. Proof of Schur decomposition theorem. Consequences for special classes of matrices.
3. Examples of solution of systems of linear algebraic equations and matrix inversion using direct methods.
4. Examples of solution of systems of linear algebraic equations using iterative methods.
5. Examples of application of methods for solution of extremal eigenvalues and complete eigenvalue problem.
6. Examples of solution of nonlinear algebraic and transcendental equations and their systems. Numerical approximation of integrals.  Goals:  Knowledge: Correct understanding of the theoretical basis for numerical algorithms is accented. Skills: Applications of numerical methods for solution of basic mathematical tasks originated from technical or scientific problems.  Requirements:   Key words:  Direct methods, iterative methods, eigenvalue problem, systems of equations, interpolation, numerical calculation of integrals
 References  Key references:
[4] A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. SpringerVerlag 2000
Recommended references:
[5] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965 

Differential Equations  01DIFR 
Beneš 
  
2+2 z,zk 
 
4 
Course:  Differential Equations  01DIFR  prof. Dr. Ing. Beneš Michal    3+1 Z,ZK    4  Abstract:  The course contains introduction in the solution of ordinary differential equations. It contains a survey of equation types solvable analytically, basics of the existence theory, solution of linear types of equations and introduction in the theory of boundaryvalue problems.  Outline:  1. Introduction  motivation in applications
2. Basics  theory of ordinary differential equations
3. Particular types of 1storder ODEs.
 separated and separable equations
 homogeneous equations
 equations with the rational argument of the righthand side
 linear equations
 Bernoulli equations
 Riccati equations
 Equations x=f(y') a y=f(y')
4. Existence theory for equations y'=f(x,y)
 Peano theorem
 Osgood theorem
5. Sensitivity on the righthand side and on the initial conditions
6. Linear nth order differential equations
7. Systems of 1st order linear differential equations
8. Boundaryvalue problems  Outline (exercises):  1. Equations with separated variables
2. Separable equations
3. Homogeneous differential equations
4. Generalized (quasihomogeneous) differential equations
5. Equations with rational righthandside argument s racionálním argumentem
6. Linear 1storder differential equations
7. Bernoulli equations
8. Riccati equations
9. Differential equations x=f(y') a y=f(y')
10. Linear nth order differential equations
with constant coefficients
11. Fundamental system for linear nth order differential equations
12. Systems of linear 1st order differential equations with constant coefficients  Goals:  Knowledge:
analytical solution of selected types of equations, the basics of the existence theory, solution of linear types of equations
Skills:
Analytical solution of the known types of ordinary differential equations, mathematical analysis of the initialvalue problems, solution of linear nth order differential equations and of the system of 1storder linear ordinary differential equations.  Requirements:  Basic course of Calculus, Linear Algebra (in the extent of the courses 01MA1, 01MAA24, 01LA1, 01LAA2 held at the FNSPE CTU in Prague).
 Key words:  Initialvalue problems for differential equations, Euler approximation, Peano theorem, fundamental system, wronskian, method of variation of constants.
 References  Key references:
[1] J. Kluvánek, L. Mišík a M. Švec. Mathematics II, SVTL Bratislava 1961 (in Slovak)
[2] K. Rektorys a kol. Survey of Applied Mathematics, Prometheus, Praha 1995 (in Czech)
Recommended references:
[3] L. S. Pontryagin, Ordinary Differential Equations. AddisonWesley, London 1962
[4] A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Chapman and Hall/CRC Press, Boca Raton, 2003
[5] M.W.Hirsch, S.Smale, Differential Equations, Dynamical systems, and Linear Algebra, Academic Press, Boston, 1974
[6] F.Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, Berlin 1990
[7] W. Walter, Gewöhnliche Differenzialgleichungen, Springer, Berlin 1990 

Calculus B3  01MAB34 
Krbálek 
2+4 z,zk 
2+4 z,zk 
7 
7 
Course:  Calculus B3  01MAB3  doc. Mgr. Krbálek Milan Ph.D.  2+4 Z,ZK    7    Abstract:  The course is devoted to functional sequences and series, theory of ordinary differential equations, theory of quadratic forms and surfaces, and general theory of metric spaces, normed and prehilbert?s spaces.  Outline:  1. Functional sequences and series  convergence range, criteria of uniform convergence, continuity, limit, differentiation and integration of functional series, power series, Series Expansion, Taylor?s theorem. 2. Ordinary differential equations  equations of first order (method of integration factor, equation of Bernoulli, separation of variables, homogeneous equation and exact equation) and equations of higher order (fundamental system, reduction of order, variation of parameters, equations with constant coefficients and special righthand side, Euler?s differential equation). 3. Quadratic forms and surfaces  regularity, types of definity, normal form, main and secondary signature, polar basis, classification of conic and quadric 4. Metric spaces  metric, norm, scalar product, neighborhood, interior and exterior points, boundary point, isolated and nonisolated point, boundary of set, completeness of space, Hilbert?s spaces.  Outline (exercises):  1. Functional sequences. 2. Functional series. 3. Power series 4. Solution of differential equations. 5. Quadratic forms. 6. Quadratic surfaces. 7. Metric spaces, normed and Hilbert?s spaces.  Goals:  Knowledge: Investigation of uniform convergence for functional sequences and series. Solution of differential equations. Classification of quadratic forms and surfaces. Classification of points of sets. Skills: Individual analysis of practical exercises.  Requirements:  Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).  Key words:  Function sequences, function series, differential equations, quadratic forms, quadratics surfaces, metric spaces, norm spaces, preHilbert spaces  References  Key references:
[1] Robert A. Adams, Calculus: A complete course, 1999,
[2] Thomas Finney, Calculus and Analytic geometry, Addison Wesley, 1996
Recommended references:
[3] John Lane Bell: A Primer of Infinitesimal Analysis, Cambridge University Press, 1998
Media and tools: MATLAB 
Course:  Calculus B4  01MAB4  doc. Mgr. Krbálek Milan Ph.D.    2+4 Z,ZK    7  Abstract:  The course is devoted properties of functions of several variables, differential and integral calculus. Furthermore, the measure theory and theory of Lebesgue integral is studied.  Outline:  Differential calculus of functions of several variables  limit, continuity, partial derivative, directional partial derivative, total derivative and tangent plane, Taylor?s theorem, elementary terms of vector analysis, Jacobi matrix, implicit functions, regular mappings, change of variables, noncartesian coordinates, local and global extremes. Integral calculus of functions of several variables  Riemann?s construction of integral, Fubiny theorem, substitution of variables. Curve and surface integral  curve and curve integral of first and second kind, surface and surface integral of first and second kind, Green and Gauss and Stokes theorems. Fundamentals of measure theory  set domain, algebra, domain generated by the semidomain, sigmaalgebra, sets H_r, K_r and S_r, Jordan measure, Lebesgue measure. Abstract Lebesgue integral  measurable function, measurable space, fundamental system of functions, definition of integral, Levi and Lebesgue theorems, integral with parameter, Lebesgue integral and his connection to Riemann and Newton integral, theorem on substitution, Fubiny theorem for Lebesgue integral.  Outline (exercises):  1. Function of several variables (properties). 2. Function of several variables (differential calculus). 3. Function of several variables (integral calculus) 4. Curve and surface integral. 5. Measure Theory 6. Theory of Lebesgue integral.  Goals:  Knowledge: Investigation of properties for function of severable variables. Multidimensional integrations. Curve and surface integration. Theoretical aspects of measure theory and theory of Lebesgue integral. Skills: Individual analysis of practical exercises.  Requirements:  Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01MAB3, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).  Key words:  Function of several variables, curve and surface integrals, measure theory, theory of Lebesgue integral  References  Key references:
[1] M. Giaquinta, G. Modica, Mathematical analysis  an introduction to functions of several variables, Birkhauser, Boston, 2009
Recommended references:
[2] S.L. Salas, E. Hille, G.J. Etger, Calculus (one and more variables), Wiley, 9th edition, 2002
Media and tools: MATLAB 

Numerical Methods 1  12NME1 
Limpouch 
  
2+2 z,zk 
 
4 
Course:  Numerical Methods 1  12NME1  prof. Ing. Limpouch Jiří CSc.    2+2 Z,ZK    4  Abstract:  There are explained the basic principles of numerical mathematics important for numerical solving of problems important for physics and technology. Methods for solution of tasks very important for physicists (ordinary differential equations, random numbers) are included in addition to the basic numerical methods. Integrated computational environment MATLAB is used as a demonstration tool. The seminars are held in computer laboratory and PASCAL is used as a principle programming language and MATLAB is also used.  Outline:  1.Numerical mathematics, truncation error, floating point representation of numbers, roundoff error
2.Correctness of problem, condition number, numerical stability; numerical libraries
3.Solution of linear equation systems  direct methods
4.Sparse matrices, iteration methods for linear equation systems; eigensystems
5.Interpolation and extrapolation, interpolation in more dimensions
6.Chebyshev approximation, Chebyshev polynomials, least square approximation
7.Evaluation of functions; sorting
8.Root finding and nonlinear set of equations
9.Search for extremes of functions
10.Numerical integration of functions
11.Random numbers and Monte Carlo integration
12.Ordinary differential equations  initial problem, stiff equations
13.Ordinary differential equations  boundary value problem
 Outline (exercises):  The seminars are held in computer laboratory and PASCAL is used as a principle programming language and system MATLAB is applied for demonstrations.
1. Floating point representation of numbers, roundoff error, condition number
2.Solution of linear equation systems  direct methods, condition number of matrix
3.Sparse matrices, iteration methods for linear equation systems; eigensystems
4.Interpolation and extrapolation, cubic spline
5.Chebyshev approximation, Chebyshev polynomials, least square approximation
6.Evaluation of functions
7.Root finding and nonlinear set of equations
8.Search for extremes of functions
9.Numerical integration of functions
10.Ordinary differential equations  initial problem, stiff equations
11.Ordinary differential equations  boundary value problem
 Goals:  Knowledge:
Basic principles of numerical mathematics important for numerical solving of problems important for physics and technology including also ordinary differential equations.
Skills:
Usage of numerical mathematics for solving of practical problems, ability to choose routines from numerical libraries and to avoid most common errors.  Requirements:   Key words:  Applied numerical mathematics, PASCAL language, MATLAB, ordinary differential equations.  References  Key references:
[1] W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling: Numerical Recipes in Pascal (The art of scientific computation), Cambridge University Press, Cambridge 1989 (also versions for C and Fortran).
Recommended references:
[2] A. Ralston, P. Rabinowicz, A First Course in Numerical Analysis, McGrawHill 1965 (reprinted by Dover Publiícations, 2001)
[3] R.W. Hamming, Numerical Methods for Scientists and Engineers, 2nd edition, Dover Publiícations 1986
Equipment:
Computer laboratory with Pascal programming language and Matlab program. 

Selected Topics in Mathematics  01VYMA 
Mikyška 
  
2+2 z,zk 
 
4 
Course:  Selected Topics in Mathematics  01VYMA  doc. Ing. Mikyška Jiří Ph.D.    2+2 Z,ZK    4  Abstract:  Fourier series: complete orthogonal systems, expansion of functions into Fourier series, trigonometric Fourier series and their convergence. Complex analysis: derivative of holomorphic functions, integral, Cauchy's theorem, Cauchy's integral formula, singularities, Laurent series, residue theorem.  Outline:  1. Theory of Fourier series in a general Hilbert space, complete orthogonal systems, Bessel inequality, Parseval equality.
2. Fourier series in L2, trigonometric system, Fourier coefficients, Bessel inequality, Parseval equality, expansion of a function into trigonometric series.
3. Criteria of convergence of Fourier series.
4. Analysis of complex functions: derivative, analytical functions, CauchyRiemann conditions.
5. Contour integral of complex functions of a complex variable, theorem of Cauchy, Cauchy's integral formula.
6. Expansion of an analytic function into a power series, isolated singularities, Laurent expansion, residue theorem.  Outline (exercises):  1. Summary of properties of function series, investigation of the uniform convergence of function series.
2. Fourier series in a general Hilbert space, GrammSchmidt ortogonalization, ortogonal polynomials.
3. Trigonometric system in L2. Expansions of trigonometric functions into trigonometric Fourier series, investigation of convergence of the trigonometric series. Summation of some series using the Fourier expansions.
4. Elementary functions of complex variables: polynomials, exponential function, goniometric functions, complex logarithm
5. Analysis in a complex domain: continuity, derivative, CauchyRiemann conditions.
6. Evaluation of contour integrals of complex functions of a complex variable, applications of the Cauchy theorem, Cauchy integral formula and residue theorem.  Goals:  Expansion of functions to the Fourier series and investigation of their convergence, application of theory of analytic functions for evaluation of curve integrals in complex plane and evaluation of some types of definite integral of real functions of a real variable.
Skills: to use expansions of functions into a Fourier series to evaluate sums of some series, evaluation of definite integrals using the theory of functions of complex variable.  Requirements:  Basic Calculus (in the extent of the courses 01MA1, 01MAA23, or 01MAB23 held at the FNSPE CTU in Prague).  Key words:  Sequences and series of functions,
Fourier series, complex analysis.  References  Key references:
[1] J. DunningDavies, Mathematical Methods for Mathematicians, Physical Scientists and Engineers, John Wiley and Sons Inc., 1982.
Recommended references:
[2] A. S. Cakmak, J. F. Botha, and W. G. Gray, Computational and Applied Mathematics for Engineering Analysis, SpringerVerlag Berlin, Heidelberg, 1987. 

Waves, Optics and Atomic Physics  02VOAF 
Tolar 
4+2 z,zk 
  
6 
 
Course:  Waves, Optics and Atomic Physics  02VOAF  prof. Ing. Tolar Jiří DrSc.  4+2 Z,ZK    6    Abstract:  Wave phenomena in mechanics and electromagnetism: modes, standing and travelling waves, wave packets in dispersive media. Wave optics: polarization, interference, diffraction, coherence. Geometrical optics. Atomic physics: black body radiation, quantum of energy, photoeffect, the Compton effect, the de Broglie waves, atomic spectra and the structure of atoms.  Outline:  11. Oscillations of systems of mass points
2. Travelling waves in nondispersive media
3. Waves in dispersive media
4.5. Energy and reflection of waves
6. Electromagnetic waves
7. Polarization
8. Interference and diffraction
9. Geometrical optics
10. Black body radiation, photons
12. de Broglie waves
13. Spectra and stationary states of atoms  Outline (exercises):  Solving examples on the following topics:
1. Oscillations of systems of mass points
2. Travelling waves in nondispersive media
3. Waves in dispersive media
4.5. Energy and reflection of waves
6. Electromagnetic waves
7. Polarization
8. Interference and diffraction
9. Geometrical optics
10. Black body radiation, photons
12. de Broglie waves
13. Spectra and stationary states of atoms  Goals:  Knowledge:
Physics of mechanical and electromagnetic oscillations and waves, foundations of atomic physics.
Skills:
Solving concrete physical and technical examples concerning oscillations and waves.  Requirements:  Course of basic physics (02MECH, 02ELMA)  Key words:  oscillations, standing waves, travelling waves, plane waves, dispersion relation, quasimonochromatic wave packets, phase velocity, group velocity, characteristic impedance, energy density, energy flux density, reflectivity, radiation pressure, polarization of light, interference, diffraction grid, diffraction on  References  Key references:
[1] F.S. Crawford, Jr.: Berkeley Physics Course 3, Waves, McGrawHill, New York 1968
[2] J. Tolar, J. Koníček: Sbírka řešených příkladů z fyziky (Vlnění), skripta ČVUT, Praha 1999
Recommended references:
[3] J. Tolar: Vlnění, optika a atomová fyzika, kap. 1.  9., viz //www.fjfi.cvut.cz, katedra fyziky
[4] H. Georgi: The Physics of Waves, Prentice Hall, Upper Saddle River NJ 1993


Thermodynamics and Statistical Physics  02TSFA 
Jex 
  
2+2 z,zk 
 
4 
Course:  Thermodynamics and Statistical Physics  02TSFA  prof. Ing. Jex Igor DrSc.    2+2 Z,ZK    4  Abstract:  Foundation of thermodynamics and statistical physics.Thermodynamic potential, the Joule Thomson effect, conditions of equilibrium, the BraunLe Chatelier principle.Statistical entropy. Basics of many body description from a statistical point of view (classical and quasiclassical regime within the frame of a canonical and grandcanonical ensemble, Fermi gas, models of crystals and the black body radiation). The Boltzmann equation is used to discusses simple transport phenomena.
 Outline:  1.Statistical entropy, the most probable distribution
2.Statistical ensembles
3.Thermodynamic potentials
4.Equilibrium conditions
5.The phase rule, phase transitions
6.Thermodynamic inequalities, BraunLe Chatelier principle
7.Statistical description and the thermodynamics of the ideal gas
8.FermiDirac, BoseEinstein statistics
9.Heat capacity of crystals
10.Black body radiation
11.Boltzmann?s transport equation
12.Boltzmann?s Htheorem, transport phenomena
 Outline (exercises):  Solving exercises on the following topics
1.Statistical entropy, the most probable distribution
2.Statistical ensembles
3.Thermodynamic potentials
4.Equilibrium conditions
5.The phase rule, phase transitions
6.Thermodynamic inequalities, BraunLe Chatelier principle
7.Statistical description and the thermodynamics of the ideal gas
8.FermiDirac, BoseEinstein statistics
9.Heat capacity of crystals
10.Black body radiation
11.Boltzmann transport equation
12.Boltzmann Htheorem, transport phenomena
 Goals:  Knowledge: learn basic concepts of thermodynamics and statictical physics
Skills: solve elementary problems of statistical physics and thermodynamics  Requirements:  mechanics, electricity and magnetism, theoretical physics
 Key words:  Thermodynamics, equilibrium conditions, statistical entropy, statistical ensembles, transport equation  References  Key references:
[1] Z. Maršák, Thermodynamics and statistical physics, ČVUT Praha, 1995 (in czech)
Recommended references:
[1] J. Kvasnica, Thermodynamics, SNTL Praha, 1965 (in czech)
[2] J. Kvasnica, Statistical physics, Academia Praha 2003 (in czech)
[3] H. B. Callen, Thermodynamics and an introduction to thermostatics, Wiley, New York, 1985


Theoretical Physics 1  02TEF12 
Hlavatý, Jex, Tolar 
2+2 z,zk 
2+2 z,zk 
4 
4 
Course:  Theoretical Physics 1  02TEF1  prof. RNDr. Hlavatý Ladislav DrSc. / prof. Ing. Jex Igor DrSc. / prof. Ing. Tolar Jiří DrSc.  2+2 Z,ZK    4    Abstract:  The course is an introduction to methods of theretical physics (nonrelativistic, classical). The course communicates basic concepts of the Lagrange formalism and the efficiency of the method illustrated on elementary examples like the two body problem, elastic scattering and the motion of rigid bodies. Advanced parts of the course cover differential and integral principles of mechanics. The course is a preparation for the course TEF2.  Outline:  1.Mathematical formalism
2.Newtonian mechanics
3.Lagrange function, constrains, generalised coordinates
4.Symmetries of the Lagrange function and conservation laws
5.Virial
6.Two body problem
7.Elastic scattering
8.Oscillations of coupled systems
9.Dynamics of rigid bodies
10.Classification of physical principles, the static equilibrium
11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz)
12.Integral principles (Hamilton, Jacobi, Maupertius)
 Outline (exercises):  Solving exercises on the following topics:
1.Mathematical formalism
2.Newtonian mechanics
3.Lagrange function, constrains, generalised coordinates
4.Symmetries of the Lagrange function and conservation laws
5.Virial
6.Two body problem
7.Elastic scattering
8.Oscillations of coupled systems
9.Dynamics of rigid bodies
10.Classification of physical principles, the static equilibrium
11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz)
12.Integral principles (Hamilton, Jacobi, Maupertius)
 Goals:  Knowledge:
Learn the basics of analytical mechanics. The subject belongs to the course of physics at FNSPE.
Skills:
Application of methods of theoretical phzsics to solve concrete examples  Requirements:  02MECH, 02ELMA  Key words:  Analytical mechanics, Lagrange formalism, Variational principles of mechanics  References  Key references:
[1] I.Štoll, J. Tolar, Theoretical Physics, ČVUT 2002 (in Czech)
Recommended references:
[1] V. Trkal, Mechanics of Mass Points and Solid Bodies, ČSAV Praha 1956 (in Czech)
[2] L.D. Landau, E.M. Lifšic, Teoreticeskaja fizika I, FIZMATGIZ Moskva, 2002 (in Russian)

Course:  Theoretical Physics 2  02TEF2  prof. RNDr. Hlavatý Ladislav DrSc. / prof. Ing. Jex Igor DrSc. / prof. Ing. Tolar Jiří DrSc.    2+2 Z,ZK    4  Abstract:  The Hamilton formalism.
The special theory of relativity: relativistic mechanics and classical field theory in the Minkowski spacetime.
Classical electrodynamics: Maxwell's equations in the Minkowski space  time, electromagnetic waves in dielectric media,
electromagnetic radiation in the dipole approximation.  Outline:  1.  3. Hamilton's formalism
4.  7. Special relativity
8.  10.Electromagnetic field
11.13. Electromagnetic waves. Electric dipole radiation  Outline (exercises):  Solving exercises on the following topics
1.  3. Hamilton's formalism
4.  7. Special relativity
8.  10.Electromagnetic field
11.13. Electromagnetic waves. Electric dipole radiation  Goals:  Knowledge:
Learn the fundamentals of Hamilton's formalism, special relativity and electrodynamics. The subject belongs to the course of physics at FNSPE.
Skills:
Application of methods of theoretical phzsics to solve concrete examples.  Requirements:  02TEF1  Key words:  Hamiltonian, Hamilton's equations, conservation laws, canonical transformations, HamiltonJacobi equation, Minkowski spacetime, interval, Lorentz transformations, equations of motion for a relativistic particle, Maxwell's equations in a medium, potentials of electromagnetic field, Maxwell's equations in Minkowski spacetime  References  Key references:
[1] I. Štoll, J. Tolar: Theoretical Physics (in Czech), ČVUT, Praha 2004
Recommended references:
[2] J.D. Jackson: Classical Electrodynamics, Wiley, New York 1962
[3] H. Goldstein, C. Poole, J. Safko: Classical Mechanics, AddisonWesley, New York 2002


Výuka jazyků  04.. 
KJ 
  
  
 
 

Introduction to Psychology  00UPSY 
Lidická 
  
0+2 z 
 
1 
Course:  Introduction to Psychology  00UPSY  PhDr. Oudová Drahomíra Ph.D.          Abstract:   Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  

Introduction to Law  00UPRA 
Čech 
  
0+2 z 
 
1 
Course:  Introduction to Law  00UPRA  Mgr. Čech Martin          Abstract:   Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  

Rhetoric  00RET 
Kovářová 
  
0+2 z 
 
1 
Course:  Rhetoric  00RET  Mgr. Kovářová Jana          Abstract:  The course is focused on the acquisition of speech and voice techniques and on the rules of correct pronounciation. The course is also devoted to the composition of public speech as well as to its nonverbal aspects. Stylistics exercises, strategies for coping with stagefright and a short excursion into the history of rhetoric are an integral part of the course.
 Outline:  1. Introduction  rhetoric  purpose, history, outline of areas linked to rhetoric;
 oral speech  purpose, listeners, environment; preparation for public speech
2. Language  "correct" form of written and spoken language; fillers; vocal and speech technique  intonation, volume, speed
3. Correct pronounciation; usage of foreign words, exercising of vocal organs
4. Composition of a speech  main points, introduction, conclusion; style a stylistics
5. Rhetorical techniques, tricks and tips; formulation; argumentation
6. Coping with stagefright, relaxation and breathing; asertivity; empathy
7. Body language (facial expressions, gesticulation, posturology, proxemics), aesthetics of public appearance (politeness, etiquette, clothing etc.)
8. Analysis of real speeches; examples; rehearsing
9. Presentation tools and their usage, advantages and disadvantages; rules for PowerPoint presentation
10. Students´ presentations + analysis, feedback
11. Students´ presentations + analysis, feedback  Outline (exercises):   Goals:  Knowledge:
Familiarizing with the rules of contentual and formal preparation for a public speech.
Skills:
Acquisition of practical skills in this area and getting a feedback.  Requirements:   Key words:  Rhetoric; body language; speaker metods  References  Key references:
[1] ŠPAČKOVÁ, A.: Moderní rétorika. Praha: Grada Publishing 2009.
Recommended references:
[1] MAŘÍKOVÁ, M.: Rétorika. Manuál komunikačních dovedností. Praha: Professional Publishing 2000.
[2] ŠMAJSOVÁ BUCHTOVÁ, B.: Rétorika. Vážnost mluveného slova. Praha: Grada Publishing 2010.
[3] HIERHOLD, E.: Rétorika a prezentace. Praha: Grada Publishing 2005.
[4] HOLASOVÁ, T.: Rétorika pro techniky. Praha: ČVUT 2004.
[5] ŠESTÁK, Z.: Jak psát a přednášet o vědě. Praha: Academia 2000.
[6] PLAMÍNEK, J.: Komunikace a prezentace. Praha: Grada Publishing 2008.
[7] PLAMÍNEK J.: Řešení problémů a umění rozhodovat. Praha: Argo 1994.
[8] HONZÁKOVÁ, M.  HONZÁK, F.  ROMPORTL, M.: Čteme je správně. Slovníček výslovnosti cizích jmen. Praha: Albatros 1996.
[9] HŮRKOVÁ, J.: Česká výslovnostní norma. Praha: Scientia 1995.
[10] CAPPONI, V.  NOVÁK, T.: Sám sobě mluvčím. Praha: Grada 1994.
[11] TEGZE, O.: Neverbální komunikace. Praha: Computer Press 2003. 

Economy in Technology  00EKOT 
Fučíková 
  
0+2 z 
 
1 
Course:  Economy in Technology  00EKOT           Abstract:  The course introduces the basics of micro and macroeconomics.  Outline:  1. Introduction to economics.
2. Market, market mechanism and its elements.
3. Theory of consumer.
4. Production and cost functions in short and long terms.
5. Income, profit.
6. Firms in perfect competition.
7. Firms in imperfect competition.
8. Factors of production and respective markets.
9. Market failures and microeconomic policies.
10. Macroeconomic agregates. Total expenditure and product.
11. Money and money market.
12. Economic growth and economic cycle.
13. Unemployment.
14. Inflation.
15. Open economy, exchange rates, outer economic balance.
16. Monetary policy.
16. Government budget, fiscal policy.
17. International trade policy.
 Outline (exercises):   Goals:  Students should understand the market mechanism and market subjects' behavior in both, model and real situation, understand basic phenomena in economy, and ways that government can use to influence the economy.  Requirements:   Key words:  microeconomics, macroeconomics, consumer, firm, perfect and imperfect competition, factors of production, product, money, economic growth, unemployment, inflation, exchange rate, external economic balance, economic policy  References  [1] Holman, R: Základy ekonomie  pro studenty vyšších odborných škol a neekonomických fakult VŠ, C.H. Beck, třetí vydání, 2015.
[2] Liška, V., Sedláček, M.: Ekonomie pro techniky, Professional publishing, třetí vydání, 2010. 
 Optional courses 
Experimental Physics 2  02EXF2 
Petráček 
2+0 zk 
  
2 
 
Course:  Experimental Physics 2  02EXF2  doc. RNDr. Petráček Vojtěch CSc.  2+0 ZK    2    Abstract:  Lecture represents an introductory course in experimental physics. Students will learn methods of measurement of basic physical quantities and methods of measurement evaluation.  Outline:  1.Measurement of temperature
2.Calorimetry, thermal expansion
3.Usage of osciloscope
4.Basic electrotechnics
5.Analog instruments
6.Measurement of inner resistance
7.Compensation methods
8.Digital instruments, analog  digital conversion
9.Dosimetry of ionizing radiation
10.Detection of nuclear radiation
11.Principles and construction of particle detectors
12.Radioactivity
13.Excursion  Outline (exercises):   Goals:  Knowledge:
Basic experimental methods and routines in broad field of physics
Abilities:
Orientation in methods of experimental physics  Requirements:  Knowledge of basic course of physics  Key words:  Measurements of physical values, osciloscope, compensation methods, dosimetry, radiation, detection, radioactivity  References  Key references:
[1] Brož: Fundamentals of Physical Measurement I., SNTL Praha 1983 (in Czech)
Recommended references:
[2] Kolektiv KF: Physical experiments I., ČVUT Praha 1989, (in Czech)
[3] Kolektiv KF: Physics I  Laboratory experiments, ČVUT Praha 1998, (in Czech) 

Experimental Laboratory 1  02PRA12 
Bielčík 
0+4 kz 
0+4 kz 
6 
6 
Course:  Experimental Laboratory 1  02PRA1  Mgr. Bielčík Jaroslav Ph.D.  0+4 KZ    6    Abstract:  Lecture is intended especially for students who intend to study some of the physical specializations of FNSPE (branch Physical Engineering, Nuclear Engineering). But it can be also attended by students interested in the other specializations. In Experimental laboratory students learn how to prepare for experiments (including work with the literature), the implementation of the measurement (acquire of different experimental procedures and routines), will teach writing the records of measurement, processing and evaluation of results. At the same time practically extend the knowledge gained in lectures on physics.  Outline:  .  Outline (exercises):  1.Cavendish experiment.
2.Elasticity, Hook´s law.
3.Air bench  The Law of Conservation of Energy, crashes.
4.Volume measurements, determination of the Poisson constant.
5.Gas thermometer, latent heat of water vaporization.
6.Surface tension, viscosity of air and oil.
7.Voltmeter, ammeter, compensator.
8. Sonar.
9.Basic acoustics experiments.
10.Driven harmonic oscillation, Pohl torsion pendulum.
11.Rotational dynamics, gyroscope.
12.Heat engine and heat efficiency.  Goals:  Knowledge:
Experimental and analytic methods, different experimental procedures
Abilities:
Application of the mentioned methods on specific physical experiments, processing and evaluation of results  Requirements:  Knowledge of basic course of physics  Key words:  Experiments on mechanics, wave physics, electrics and magnetism  References  Key references:
[1] Kolektiv KF: Physics I  Laporatory excersisies, ČVUT Praha 1998 (in Czech)
Recommended references:
[2] J.D.Wilson, C.A.Hernandez: Physics Laboratory Experiments, Brooks Cole Boston 2004
Media and tools:
laboratory of the department of physics 
Course:  Experimental Laboratory 2  02PRA2  Mgr. Bielčík Jaroslav Ph.D.    0+4 KZ    6  Abstract:  Lecture is intended especially for students who intend to study some of the physical specializations of FNSPE (branch Physical Engineering, Nuclear Engineering). But it can be also attended by students interested in the other specializations. In Experimental laboratory students learn how to prepare for experiments (including work with the literature), the implementation of the measurement (acquire of different experimental procedures and routines), will teach writing the records of measurement, processing and evaluation of results. At the same time practically extend the knowledge gained in lectures on physics.  Outline:   Outline (exercises):  1.Capacity, electrostatic field.
2.Ferromagnetic hysteresis.
3.RLC circuits, driven and dumped oscillations.
4.Line spectra of Hg and Na spectral lamps using prism spectrometer.
5.Rtg spectrum of Mo anode.
6.Geometrical optics.
7.Microwawes.
8.Polarization of light.
9.Interference and diffraction of light.
10.Thermoemission of electrons.
11.Specific electron charge, energy loss of alpha particles in gases.
12.Spectrum of gamma radiation.  Goals:  Knowledge:
Advanced experimental and analytic methods and experimental procedures
Abilities:
Application of the mentioned methods on specific physical experiments, processing and evaluation of results  Requirements:  Knowledge of basic course of physics  Key words:  Experiments on wave physics, thermodynamics and nuclear physics  References  Key references:
[1] Kolektiv KF: Physics I  Laporatory excersisies, ČVUT Praha 1998 (in Czech)
Recommended references:
[2] J.D.Wilson, C.A.Hernandez: Physics Laboratory Experiments, Brooks Cole Boston 2004
Media and tools:
laboratory of the department of physics 

Programming in C++ 1  18PRC12 
Virius 
4 z 
4 kz 
4 
4 
Course:  Programming in C++ 1  18PRC1  doc. Ing. Virius Miroslav CSc.  2+2 Z    4    Abstract:  This course covers mainly the C programming language and nonobject oriented features of the C++ language.  Outline:  1.Introductory examples
2.Compilation, project
3.Basic constructs
4.Scalar data types in C and C++
5.Expressions
6.Statements
7.Pointers, arrays and pointer arithmetics
8.Structs and unions
9.Functions
10.Preprocessor
11.Standard C library  Outline (exercises):  The sylabus of the excercises is the same as the sylabus of the lecture.  Goals:  Knowledge:
The C programming language according to the ISO 9899:1990 and ISO 9899:1999 international standards and selected features of the C++ programming language.
Ability:
The student will be able to use this programming language to solve common programming tasks.  Requirements:  Basic programming skills (as covered by the "Basic of programming" course)  Key words:  C programming language;compilation;basic data type;lexical convention;array;pointer;pointer arithmetic;struct;union;statement;preprocessor;macro;C runtime library;memory management  References  Key references:
[1] Virius, M: Programování v C++, 3. vyd. Praha, Vydavatelství ČVUT 2009. ISBN 9788001043714
Recommended references:
[1] Stroustrup, B.: The C++ Programming Language. 3rd edition. AddisonWesley 1997. ISBN 0201889544.
[2] Virius, M. Pasti a propasti jazyka C++. Druhé vydání. Brno, Computer Press 2005. ISBN 8025105091.
[3] Eckel, B. Myslíme v jazyku C++. Praha, Grada Publishing 2000. ISBN 8024790092. 552 stran. (První díl)
[4] Sutter, H. Exceptional C++. AddisonWesley 2000. ISBN 0201615622.
[5] Sutter, H. More Exceptional C++. AddisonWesley 2002. ISBN 020170434X.
[6] Koenig, A. C Traps and Pitfalls. AddisonWesley 1989. ISBN 0201189288. 
Course:  Programming in C++ 2  18PRC2  doc. Ing. Virius Miroslav CSc.    2+2 KZ    4  Abstract:  This course covers the object oriented programming and othesr advanced constructs in the C+;+ programming language and the Standard Template Library.  Outline:  1. Class (object) types in C++
1.1 Declaraion of the class type without ancestors
1.2 Fields and methods. constructors.
1.3 Copy constructor. Destructor.
1.4 Inner class.
1.5 Inheritance, virtual methods.
1.6 Identifier conflicts.
1.7 Virtual inheritance.
1.8 Union as object type.
1.9 Member pointers.
2. Operator overloading
2.1 Common operator overloading.
2.2 Operators overloadable as methods only.
2.3 Operators new and delete.
3. Templates
3.1 Declaration, parameters.
3.2 Class type templetes
3.3 Function templates
3.4 Template metaprogramming
4. Exceptions.
5. Run time type identification.
6. Namespaces.
7. Input/output by stream classes.
8. STL: containers, localization tools.  Outline (exercises):  Excercises outline and sylabus is the same as the outline and sylabus of the lecture  Goals:  Knowledge:
The C++ programming language according to the ISO 14882:2003 international standard (including the proposed new version of the standard).
Ability:
Usage of the advanced constructs of the C++ programming language for the solution of the common programming tasks.  Requirements:  Programming in C++ 1  Key words:  class;struct;union;constructor;destructor;method;field;operator;operator overloading;template;tenmplate metaprogramming;exception;run time type identification;namespace;STL;inheritance;virtual inheritance  References  Key references:
[1] Virius, M: Programování v C++, 3. vyd. Praha, Vydavatelství ČVUT 2009. ISBN 9788001043714
Recommended references:
[1] Stroustrup, B.: The C++ Programming Language. 3rd edition. AddisonWesley 1997. ISBN 0201889544.
[2] Virius, M. Pasti a propasti jazyka C++. Druhé vydání. Brno, Computer Press 2005. ISBN 8025105091.
[3] Eckel, B. Myslíme v jazyku C++. Praha, Grada Publishing 2000. ISBN 8024790092. 552 stran. (První díl)
[4] Sutter, H. Exceptional C++. AddisonWesley 2000. ISBN 0201615622.
[5] Sutter, H. More Exceptional C++. AddisonWesley 2002. ISBN 020170434X.
[6] Koenig, A. C Traps and Pitfalls. AddisonWesley 1989. ISBN 0201189288.


Practical Informatics for Technics 2  12PIN23 
Šiňor 
1+1 z 
1+1 z 
2 
2 
Course:  Practical Informatics for Technics 2  12PIN2  doc. Dr. Ing. Šiňor Milan  1+1 Z    2    Abstract:  Practically oriented three semester course of basics and applications of informatics for science and engineering included as obligatory alternative course. Constituent part is realized in computer classrooms. The second part of the course is "Introduction to computer algebra systems?.
 Outline:  Difficulties of scientific computing, algebraic and numerical computation, graphics. Computer algebra systems Maple, Mathematica and Maxima. Symbolic expressions, variables, functions and procedures. Simplification and manipulation with expressions, equations and systems of equations, fields and matrices. Symbolic derivative, integration, series, differential equations. Visualizations and animations. Elementals of programming in Maple and Mathematica.
 Outline (exercises):  Difficulties of scientific computing, algebraic and numerical computation, graphics. Computer algebra systems Maple, Mathematica and Maxima. Symbolic expressions, variables, functions and procedures. Simplification and manipulation with expressions, equations and systems of equations, fields and matrices. Symbolic derivative, integration, series, differential equations. Visualizations and animations. Elementals of programming in Maple and Mathematica.
 Goals:  Knowledge:
The goal is to provide prospective engineers with such knowledges of computer technology and informatics that are at present necessary for effective practice of professional activities.
Skills:
Constituent part is realized in computer classrooms as practical exercises. This leads to acquirement of experience gained.
 Requirements:   Key words:  Algebraic and numerical computation. Computer algebra systems, Maple, Mathematica, Maxima. Symbolic manipulations, graphics.  References  Key references:
[1] Maple 14 Full Manual Set, Maplesoft 2010.
Recommended references:
[2] S. Wolfram: The Mathematica Book, Fifth Edition. Wolfram Media 2003. 
Course:  Practical Informatics for Technics 3  12PIN3  doc. Dr. Ing. Šiňor Milan    1+1 Z    2  Abstract:  Practically oriented three semester course of basics and applications of informatics for science and engineering included as obligatory alternative course. Constituent part is realized in computer classrooms. The third part of the course is "Introduction to scientific computing?.  Outline:  Interpreted and compiled languages: Interpreted languages Matlab, Scilab and Python as instruments for scientific computing. Scalar data types, declaration, operators and expressions. Functions, arrays, libraries, compound data types.
Basic terms and numerical algorithms: Number representation, range and number of significant digits, IEEE arithmetics, rounding error, interval arithmetics, error accumulation. Solution of nonlinear equations, bisection method, Newton's method. Numerical integration, rectangular and trapezoid method. Basic solution of ordinary differential equations, Euler method and its modification.
Scientific documents and computer presentations: Particularity of scientific documents, text processors for scientific documents, mathematical text and graphics. Resources for DTP, typography system TeX. PostScript language.
 Outline (exercises):  Interpreted and compiled languages: Interpreted languages Matlab, Scilab and Python as instruments for scientific computing. Scalar data types, declaration, operators and expressions. Functions, arrays, libraries, compound data types.
Basic terms and numerical algorithms: Number representation, range and number of significant digits, IEEE arithmetics, rounding error, interval arithmetics, error accumulation. Solution of nonlinear equations, bisection method, Newton's method. Numerical integration, rectangular and trapezoid method. Basic solution of ordinary differential equations, Euler method and its modification.
Scientific documents and computer presentations: Particularity of scientific documents, text processors for scientific documents, mathematical text and graphics. Resources for DTP, typography system TeX. PostScript language.
 Goals:  Knowledge:
The goal is to provide prospective engineers with such knowledges of computer technology and informatics that are at present necessary for effective practice of professional activities.
Skills:
Constituent part is realized in computer classrooms as practical exercises. This leads to acquirement of experience gained.
 Requirements:   Key words:  Interpreted and compiled languages for scientific computing. Basic terms and numerical algorithms.
Typography system for TeX scientific documents.  References  Key references:
[1] D. C. Hanselman, B. Littlefield: Mastering Matlab 7. Prentice Hall 2004.
Recommended references:
[2] L. Lamport: LaTeX: A Document Preparation System (2nd Edition). AddisonWesley 1994.


Dosimetry Seminar 1  16SED12 
Johnová 
0+2 z 
0+2 z 
2 
2 
Course:  Dosimetry Seminar 1  16SED1  Ing. Johnová Kamila          Abstract:  Introductory lectures on physics and dosimetry of ionizing radiation followed by lectures about routine and research activities in the field.  Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  
Course:  Dosimetry Seminar 2  16SED2  Ing. Johnová Kamila          Abstract:  Presentation of graduates and students on research topics in the field of dosimetry and medical physics.  Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  

Seminar on Calculus B1  01SMB12 
Krbálek 
0+2 z 
0+2 z 
2 
2 
Course:  Seminar on Calculus B1  01SMB1  doc. Mgr. Krbálek Milan Ph.D.  0+2 Z    2    Abstract:  The course is devoted to support the lectures of Calculus B3.  Outline:  Physical applications of theory of differential equation, general properties of metric, norm and prehilbert spaces, Hilbert spaces of functions.  Outline (exercises):  Physical applications of theory of differential equation, general properties of metric, norm and prehilbert spaces, Hilbert spaces of functions.  Goals:  Knowledge: Application of mathematical theory to the practical tasks. Skills: Individual analysis of practical exercises.  Requirements:  Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).  Key words:  Solution of differential equations, metric spaces, normed and Hilbert?s spaces.  References  Key references:
[1] Robert A. Adams, Calculus: A complete course, 1999,
[2] Thomas Finney, Calculus and Analytic geometry, Addison Wesley, 1996
Recommended references:
[3] John Lane Bell: A Primer of Infinitesimal Analysis, Cambridge University Press, 1998
Media and tools: MATLAB 
Course:  Seminar on Calculus B2  01SMB2  doc. Mgr. Krbálek Milan Ph.D.    0+2 Z    2  Abstract:  The course is devoted to support the lectures of Calculus B4.  Outline:  Regular mappings in two or threedimensional space, analytical forms of tangent hyperplanes to quadrics and pseudoquadrics, volumes of chosen bodies, derivative of integral with parameter, application of measure theory and theory of Lebesgue integral.  Outline (exercises):  Regular mappings in two or threedimensional space, analytical forms of tangent hyperplanes to quadrics and pseudoquadrics, volumes of chosen bodies, derivative of integral with parameter, application of measure theory and theory of Lebesgue integral.  Goals:  Knowledge: Application of mathematical theory to the practical tasks. Skills: Individual analysis of practical exercises.  Requirements:  Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01MAB3, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).  Key words:  Function of several variables, measure theory, theory of Lebesgue integral  References  Key references:
[1] M. Giaquinta, G. Modica, Mathematical analysis  an introduction to functions of several variables, Birkhauser, Boston, 2009
Recommended references:
[2] S.L. Salas, E. Hille, G.J. Etger, Calculus (one and more variables), Wiley, 9th edition, 2002
Media and tools: MATLAB 

Physical Training 1  00TV12 
ČVUT 
 z 
 z 
1 
1 
Course:  Physical Training 1  00TV1           Abstract:   Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  
Course:  Physical Training 2  00TV2           Abstract:   Outline:   Outline (exercises):   Goals:   Requirements:   Key words:   References  
 