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: 

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 
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. 390430 
Ordinary differential equations: Definitions and examples. Ex.: 2,3,5,9,H1,H4. 
Seminar 2: p. 233236, 666687 
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. 1426 in Lecture Notes). 
Seminar 4: p. 340376 
Fourier analysis: Fourier series. Fourier coefficients. Average values. Parseval's theorem. 
Seminar 5:  Fourier analysis: Problems. Ex. 20,2325, H21,H22. 
Seminar 6: p. 633637 
Separation of variables. Wave equation. Vibrating string. 
Seminar 7: p. 628631 
Wave and heat flow equations: Problems. Ex.: 27,29,30,31,H26,H28. 
Seminar 8: p. 521524 
Laplace operator in cylindrical and spherical coordinates. Ex.: 32,33,34. 
Seminar 9: p. 587604 
Laplace equation in cylindrical coordinates: Bessel functions and their properties. 
Seminar 10: p. 638646 
Laplace equation in cylindrical coordinates: FourierBessel series.Ex.: 35,36. 
Seminar 11: 
Harmonic functions and potential problem ( p. 7784 in Lecture Notes). Ex.: 37,38,39. 
Seminar 12:  Potential theory. Polar and spherical coordinates. Ex.: 40,43,44,H41,H42. 
Seminar 13: p. 562581 
Laplace equation in spherical coordinates: Legendre polynomials and their properties. 
Seminar 14: p. 583584 
Laplace equation in spherical coordinates: Associative Legendre polynomials. 
Seminar 15: p. 571573 
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. 110114). 
Seminar 17: p. 609611 
Analysis of radial part of Schr�inger equation for hydrogen atom (in Lecture Notes p. 117120). Energy eigenvalues and Laguerre polynomials. 
Seminar 18: p. 567 576, 647650, 655656. 
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. 378383, 447448 
Fourier transforms. 
Seminar 21: p. 660661 
Fourier transforms: solution of temperature problem. Ex.: 57,59,60,H58. 
Seminar 22: p. 437446,659660 
Laplace transform.Ex.: 61,62,63. 
Seminar 23: p.461464 
Green's functions. 
Seminar 24:  Repetition and summary. Ex.: 6469. 