UF03600 Mathematical Methods in Physics

Faculty of Philosophy and Science in Opava
Summer 2015
Extent and Intensity
3/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Josef Juráň, Ph.D. (lecturer)
RNDr. Martin Blaschke, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Prerequisites (in Czech)
Absolvování základního kurzu matematiky pro bakalářskou fyziku.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is focused to obtain an overview about basic mathematical methods used in Physics. The core of the course lays in the following parts of mathematics: introduction to functional analysis, complex analysis, equations of mathematical physics, introduction to theory of distributions and group theory. The mathematical techniques and methods gained from previous mathematical courses are also applied. An emphasis is put on understanding of the concept, calculation skills and applications in Physics.
Syllabus
  • Selective parts of functional analysis: Banach and Hilbert spaces, linear
    operators and functionals and their applications basis of calculus of
    variations Fourier series.
    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 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.
Literature
    required literature
  • Kvasnica, J. Matematický aparát fyziky. Academia, 2004. ISBN 80-200-0603-6. info
  • Děmidovič Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 2003. ISBN 80-7200-587-1. info
    recommended literature
  • Čihák Pavel a kolektiv. Matematická analýza pro fyziky (V). Praha, 2003. ISBN 80-86732-12-6. info
  • Kopáček Jiří a kolektiv. Příklady z matematiky pro fyziky [V]. Praha, 2003. ISBN 80-86732-15-0. info
  • Arfken George B., Weber Hans J. Mathematical methods for physicists. 2001. info
  • Rektorys Karel a spolupracovníci. Přehled užité matematiky I, II. Praha, 2000. info
  • Riley K.F., Hobson M.P., Benc. Mathematical methods for physics and engineering. 1998. info
  • Bartsch Hans-Jochen. Matematické vzorce. Praha, 1987. info
Teaching methods
One-to-One tutorial
Monological (reading, lecture, briefing)
Internship
Students' self-study
Assessment methods
Test
Written exam
Credit
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
* attendance in lectures and tutorials, active participation
and/or self-study of selected parts of recommended literature (homeworks)
* a few short written tests during semester (success rate 50 %)
* written and oral exam
The course is also listed under the following terms Summer 1994, Summer 1995, Summer 1996, Summer 1997, Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014.
  • Enrolment Statistics (recent)
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