1. komponenta

Lecture type	Total

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: Course goals are to acquire theoretical and practical knowledge in the theory of ordinary and partial differential equations.

COURSE DESCRIPTION AND SYLLABUS:
1. Ordinary differential equations
2. Linear differential equations. Linear differential equations of the first order
3. Existence and uniqueness theorems for the Cauchy problem for the homogeneous linear equation of n-th order
4. Linear independence of functions and the Wronskian
5. Linear differential equation with constant coefficients
6. Nonhomogeneous differential equations. The method of undetermined coefficients. The method of Variation of Parameters.
7. Solving differential equations by power series.
8. Second order linear differential equation with regular singularities
9. Legendre polynomials and Legendre differential equation. A Generating Function for Legendre Polynomials.
10. The associated Legendre functions. Spherical harmonics
11. Laplace's equation. The method of separation of variables
12. Wave equation
13. Bessel functions and Bessel differential equation
14. Schrodinger equation. Laguerre polynomials