FPF:UFTF002 Mathematical Methods in Physic - Course Information

UFTF002 Mathematical Methods in Physics

Extent and Intensity

3/2/0. 7 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

Graduated in basic course of mathematics for Bachelor of Physics.

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

• Theoretical Physics (programme FPF, N1701 Fyz)

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. ISBN 80-7196-179-5. info
• Riley K.F., Hobson M.P., Bence S.J. 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

• Enrolment Statistics (Summer 2015, recent)
  
• Permalink: https://is.slu.cz/course/fpf/summer2015/UFTF002