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Course, academic year 2022/2023
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Mathematics for Physicists II - NMAF004
Title: Matematika pro fyziky II
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2008
Semester: summer
E-Credits: 10
Hours per week, examination: summer s.:4/3, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Co-requisite : NMAF003
Incompatibility : NMAA003, NMAA004, NMAI049, NMAI050, NUMP005, NUMP006
Is co-requisite for: NMAF005
Annotation -
Last update: T_KMA (13.05.2003)
Basic mathematics course for 2nd year students of physics. Prerequisities: Mathematical analysis I+II and Linear algebra I+II.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Kopáček, J. a kol.: Matematika pro fyziky, díly III-V, skriptum MFF UK

Syllabus -
Last update: T_KMA (13.05.2003)

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. Conformal mapping.

Fouries series - trigonometric series, pointwise and uniform convergence, orthogonality, completeness. Bessel inequality, Parseval inequality. Criteria of convergence. L^2 space, Hilbert space, Fourier series in Hilbert space.

Fourier and laplace transform - definition, properties, calculus.

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