Selected Topics of Mathematical Physics


Winter Semester 2019/2020


Lecture: M. A. Efremov

Tuesday: 10:00-13:00 N23/2622

Exercises will be delivered during the lecture. 


Description

This special lecture series aims at providing students with a Bachelor or Master degree with advanced mathematical tools to solve different problems faced by physicists, engineers, and applied mathematicians. They include (i) the Fourier method for partial differential equations (diffusion, wave, and etc.), (ii) method of integral transformations, (iii) the Green's function and its applications, (iv) integral equations, etc. Each method is illustrated by both well-known and completely new examples of physics problems appearing within classical and quantum approaches.

Contents

  • Partial differential equations
  • Fourier method and special functions
  • Method of integral transformation
  • Green's function and its applications
  • Classical orthogonal polynomials
  • Integral equations

Literature

  • P. M. Morse and H. Feshbach, Methods of Theoretical Physics (1953)
  • G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical methods for physicists (2012)
  • A. N. Tikhonov and A. A. Samarskii, Equations of mathematical physics (2011)
  • E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (1948)
  • R. Courant and D. Hilbert, Methods of mathematical physics (2009)
  • R. P. Agarwal and D. O'Regan, Ordinary and partial differential equations : with special functions, Fourier series, and boundary value problems (2009)
  • A. Sommerfeld, Partial differential equations in physics (1967)
  • J. Jost, Partial differential equations (2002)
  • L. C. Evans, Partial differential equations (2010)

Requirements for passing this modul: written examination, 50 % of exercise points