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Course, academic year 2024/2025
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Mathematics for Physicists II - NOFY162
Title: Matematika pro fyziky II
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Dušan Pokorný, Ph.D.
prof. Mgr. Milan Pokorný, Ph.D., DSc.
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Incompatibility : NMAF062
Interchangeability : NMAF062
Is incompatible with: NMAF062
Is interchangeable with: NMAF062
Annotation -
Basic mathematics course for 2nd year students of physics. Prerequisities: Mathematics for physicists I, NOFY161.
Last update: Kudrnová Hana, Mgr. (30.06.2020)
Aim of the course -

Basic mathematics course for 2nd year students of physics. Prerequisities: Mathematics for physicists II.

Last update: Kudrnová Hana, Mgr. (20.05.2019)
Literature - Czech
  • Kopáček, J.: Matematická analýza pro fyziky IV, Praha, Matfyzpress, 2010
  • Kopáček, J.: Příklady z matematiky pro fyziky IV, Praha, Matfyzpress, 2003
  • Záznamy přednášek
Last update: Kudrnová Hana, Mgr. (20.05.2019)
Teaching methods - Czech

přednáška + cvičení

Last update: Kudrnová Hana, Mgr. (20.05.2019)
Requirements to the exam - Czech

Zkouška bude písemná (početní část) a ústní (teoretická část). Student musí úspěšně složit obě části zkoušky.

Požadavky u zkoušky odpovídají sylabu předmětu v rozsahu, který byl probrán na přednášce a cvičení.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (07.02.2023)
Syllabus -
1. Introduction to the complex analysis:
Holomorfic function, Cauchy-Riemann equations, line integral in the complex domain, primitive function. Cauchy theorem, Cauchy formula, Liouville theorem. Taylor series, function holomorfic between circular contours, isolated singularities, Laurent series. Residue and Residue theorem.

2. Fourier transform of functions
Definition and basic properties. Schwartz space, L1 and L2 theory, inversion theorems, convolution, application to ODE and PDE.

3. Distributions
space D(Ω), topology, continuous linear functionals on D(Ω), order of distributions, convergence on D′(Ω), support of distributions, characterization of distributions of order 0 and non-negative distributions, derivative of distributions and its properties, approximation of δ-distributions by functions, Fourier series, Poisson summation formula, composition of distributions with diffeomorfisms, distributions with compact and point support, homogeneous distributions and their normalization.

4. Tempered distributions, integral transform of distributions
space of tempered distributions, convergence on S(R^N) and on S′(R^N), Fourier transform of tempered distributions, basic properties, tensor product of distributions and tempered distributions, convolution of distributions and tempered distributions, their Fourier transform, non-integer derivative, Fourier transform of selected distributions, Paley–Wiener theorem and its consequence, Fourier transform of radially symmetric funtions and distributions, surface measure.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (07.02.2023)
 
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