Course: Mathematical Methods in Physics

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Course title Mathematical Methods in Physics
Course code UF/TF002
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 7
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • JURÁŇ Josef, RNDr. Ph.D.
  • BLASCHKE Martin, Mgr. Ph.D.
Course content
Selective parts of functional analysis: Banach and Hilbert spaces, linear operators and functionals and their applications basis of calculus of variations. Theory of functions of a complex variable: Analytic functions, Cauchy's integral theorem and Cauchy's integral formula, residue theorem, Laurent series injective domains and inverse functions. Equations of mathematical physics: Classification of differential equations, standard and generalized solutions, Laplace and Poisson equations, wave equation, heat equation; Fourier series, Fourier and Laplace transformations; special functions. Basis of theory of distributions: Definitions, operations with distributions, Dirac delta distribution and its properties, convolution of distributions; differential equations with distributions. Group theory: Groups and their representation, groups of symmetries SU(2) and SU(3), physical applications.

Learning activities and teaching methods
One-to-One tutorial, Monological (reading, lecture, briefing), Internship, Students' self-study
Recommended literature
  • Arfken George B., Weber Hans J. Mathematical methods for physicists. 2001.
  • Bartsch Hans-Jochen. Matematické vzorce. Praha, 1987.
  • Čihák Pavel a kolektiv. Matematická analýza pro fyziky (V). Praha, 2003. ISBN 80-86732-12-6.
  • Děmidovič Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 2003. ISBN 80-7200-587-1.
  • Kopáček Jiří a kolektiv. Příklady z matematiky pro fyziky [V]. Praha, 2003. ISBN 80-86732-15-0.
  • Kvasnica, J. Matematický aparát fyziky. Academia, 2004. ISBN 80-200-0603-6.
  • Rektorys Karel a spolupracovníci. Přehled užité matematiky I, II. Praha, 2000. ISBN 80-7196-179-5.
  • Riley K.F., Hobson M.P., Bence S.J. Mathematical methods for physics and engineering. 1998.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses 1 Summer