UFTF002 Mathematical Methods in Physics

Faculty of Philosophy and Science in Opava
Summer 2021
Extent and Intensity
3/2/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Filip Blaschke, Ph.D. (lecturer)
RNDr. Josef Juráň, Ph.D. (lecturer)
RNDr. Filip Blaschke, Ph.D. (seminar tutor)
RNDr. Martin Blaschke, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Timetable
Mon 11:25–13:50 B4
  • Timetable of Seminar Groups:
UFTF002/A: Thu 9:45–11:20 B1, F. Blaschke
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
Course objectives
The course aims to introduce the most important and common mathematical methods used in physics. The content of the course has several independent themes that are explored in great detail. The acquirement of computational skills is emphasized.
Learning outcomes
After completion of this course, the student gains:
- the ability to solve the recurrent equations and calculate sums.
- basic orientation in complex analysis.
- the ability to solve general linear differential equations.
- the superpower of asymptotic analysis.
Syllabus
  • List of topics:
    - Introduction to discrete calculus. Primitive function theorem, inverse operator to improper summation. Discrete product and its inverse. Solutions to simple recurrent equations.
    - Binomial numbers and related identities. Representation as a complex integral and solution to summation identities.
    - Introduction to complex analysis. Analytic function, Riemann-Cauchy conditions. Cauchy theorem. Classification of singularities in the complex plane. Laurent series and REsidue theorem. Finding solutions to real integrals via methods of complex analysis.
    - Solving general linear second-order differential equations. Classification of singular points. Taylor series solutions. Airy function.
    - Frobenius series in regular-singular point.
    - Introduction to asymptotic methods. Definition of asymptotic relation. Method of dominant balance.
    - Perturbation series and its convergence. Summation of divergent series. Pade approximation.
    - Introduction to WKB method. Approximative solutions to differential equations.
    - Asymptotic analysis of Sturm-Liouville problem. Solving Schroedinger equation with a single turning point. Global approximation.
    - WKB approximation of Schroedinger equation with two turning points and semiclassical quantization condition.
    - Exact solutions of the Schroedinger equation with special potentials.
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
  • R. L: Graham, D. E. Knuth and O. Patashik: Concrete Mathematics, Addison-Wesley Publishing Company, 1990
  • I, C. M. Bender and S. A. Orszag: Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999
  • 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)
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 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2022, Summer 2023, Summer 2024.
  • Enrolment Statistics (Summer 2021, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2021/UFTF002