Information on the course TFYA18 Mathematical Methods of Physics, 6 ECTS points

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Advancement level: C
Aim: The course is aimed at making the students familiar with the basic equations of the mathematical physics and the methods of their solutions. The emphasis will be on the most frequently used partial differential equations and the special functions involved in the solution of these equations.
Course literature:
  1. Mary L. Boas. Mathematical methods in the physical sciences. Third edition, John Wiley and Sons, 2005.
  2. I. Yakimenko. Lecture notes in Mathematical Methods in Physics (2008).
  3. I. Yakimenko. Set of Problems in Mathematical Methods in Physics (2008). You can buy it in Linus & Linnea AB.
Course organization: The course contains 24 seminars with the theory and solution of problems following a special plan. Course will be given by Iryna Yakymenko. Course language is English.
Prerequisites: Analysis, Linear algebra, Vector analysis, Complex analysis, Fourier analysis.
Exam: A written examination with questions in theory and solution of problems.
Course language: English

Plan of Seminars:

The theory will be expounded following the book Mary L. Boas. Mathematical methods in the physical sciences (see page numbers for each seminar). The examples are from the book I. Yakimenko. Set of Problems in Mathematical Methods in Physics (H corresponds to home problems).

Seminar 1:
p. 390-430
Ordinary differential equations: Definitions and examples. Ex.: 2,3,5,9,H1,H4.
Seminar 2:
p. 233-236, 666-687
Ordinary differential equations (continuation). Differentiation and evaluation of integrals. Ex.: 13,14,15,17,18,19,H6,H7,H9,H12,H16,H19.
Seminar 3: Partial differential equations: wave, diffusion, heat flow, Laplace, Poisson and Schrodinger equations. Initial and boundary conditions. Elliptic, hyperbolic and parabolic equations (p. 14-26 in Lecture Notes).
Seminar 4:
p. 340-376
Fourier analysis: Fourier series. Fourier coefficients. Average values. Parseval's theorem.
Seminar 5: Fourier analysis: Problems. Ex. 20,23-25, H21,H22.
Seminar 6:
p. 633-637
Separation of variables. Wave equation. Vibrating string.
Seminar 7:
p. 628-631
Wave and heat flow equations: Problems. Ex.: 27,29,30,31,H26,H28.
Seminar 8:
p. 521-524
Laplace operator in cylindrical and spherical coordinates. Ex.: 32,33,34.
Seminar 9:
p. 587-604
Laplace equation in cylindrical coordinates: Bessel functions and their properties.
Seminar 10:
p. 638-646
Laplace equation in cylindrical coordinates: Fourier-Bessel series.Ex.: 35,36.
Seminar 11:
Harmonic functions and potential problem ( p. 77-84 in Lecture Notes). Ex.: 37,38,39.
Seminar 12: Potential theory. Polar and spherical coordinates. Ex.: 40,43,44,H41,H42.
Seminar 13:
p. 562-581
Laplace equation in spherical coordinates: Legendre polynomials and their properties.
Seminar 14:
p. 583-584
Laplace equation in spherical coordinates: Associative Legendre polynomials.
Seminar 15:
p. 571-573
Appliocation of Legendre polynomials in potential theory. Ex.: 45,46,47 H47,H49.
Seminar 16: Schr�inger equation for hydrogen atom (in Lecture Notes, p. 110-114).
Seminar 17:
p. 609-611
Analysis of radial part of Schr�inger equation for hydrogen atom (in Lecture Notes p. 117-120). Energy eigenvalues and Laguerre polynomials.
Seminar 18:
p. 567- 576, 647-650, 655-656.
Legendre polynomials. Potential and temperature problem with spherical symmetry.Ex.: H50, H51.
Seminar 19: Schr�inger equation: Solution of problems. Ex.: 52,54,56, H53.
Seminar 20:
p. 378-383, 447-448
Fourier transforms.
Seminar 21:
p. 660-661
Fourier transforms: solution of temperature problem. Ex.: 57,59,60,H58.
Seminar 22:
p. 437-446,659-660
Laplace transform.Ex.: 61,62,63.
Seminar 23:
p.461-464
Green's functions.
Seminar 24: Repetition and summary. Ex.: 64-69.