UFDF016 Mathematical Methods in Physics

Faculty of Philosophy and Science in Opava
Summer 2014
Extent and Intensity
0/0. 0 credit(s). Type of Completion: dzk.
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
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, standard and generalized
    solutions, Laplace and Poisson equations, wave equation, heat equation
    special functions.
    Basis of theory of distributions: Definitions, operations with distributions,
    convolution Fourier and Laplace transformations.
    Group theory: Groups and their representation, physical applications.
Language of instruction
Czech
Further Comments
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 Winter 2000, Summer 2001, Winter 2001, Summer 2002, Winter 2002, Summer 2003, Winter 2003, Summer 2004, Winter 2004, Summer 2005, Winter 2006, Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Winter 2021, Summer 2022.
  • Enrolment Statistics (Summer 2014, recent)
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