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Course, academic year 2019/2020
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Mathematics for Physicists II - NMAF062
Title in English: Matematika pro fyziky II
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. Mgr. Milan Pokorný, Ph.D.
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Interchangeability : NMAF043
In complex pre-requisite: NMAA121
Annotation -
Last update: T_KMA (13.05.2008)
Basic mathematics course for 2nd year students of physics. Prerequisities: Mathematics for physicists I, NMAF061.
Aim of the course -
Last update: T_KMA (13.05.2008)

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

Literature - Czech
Last update: doc. RNDr. Helena Valentová, Ph.D. (11.01.2018)
  • Kopáček, J.: Matematická analýza pro fyziky IV. (skripta)
  • Kopáček J.: Příklady z matematiky pro fyziky IV. (skripta)
  • Videozáznamy přednášek
Teaching methods - Czech
Last update: T_KMA (13.05.2008)

přednáška + cvičení

Requirements to the exam - Czech
Last update: doc. Ing. Branislav Jurčo, CSc., DSc. (11.01.2019)

Zkouška bude písemná a bude mít 2 části, početní a teoretickou. Student musí úspěšně složit obě části zkoušky.

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

Syllabus -
Last update: T_KMA (13.05.2008)

1. Fourier series

Trigonometric polynomials and series. Riemann-Lebesgue lemma, Riemann theorem on localization, Dirichlet kernel, pointwise properties of Fourier series, Fourier series in Hilbert spaces, Bessel inequality and Parseval equality. Orthogonal systems of polynomials (Legendre, Hermite, Chebyshev), eigenfunctions of differential operators.

2. 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.

3. Fourier transform of functions

Definition and basic properties. Schwartz space, L1 and L2 theory, inversion theorems, convolution, application to ODE and PDE.

 
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