1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

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

COURSE AIMS AND OBJECTIVES: Introduction to the mathematical theory: existence and uniqueness results of initial value problems. Introduction to numerical methods. Formulation and simulation of selected 'real life' problems using existing software.

COURSE DESCRIPTION AND SYLLABUS:
[1-4] Systems of the first order ordinary differential equtions, local existence and uniqueness of solution of initial value problem (Picard's theorem and Gronwall's lemma). Introduction to numerical methods. Autonomous equations, examples.
[5-8] Systems of linear first order equtions, fundamental matrix, global existence result, examples. The Laplace transformation, n-th order equation, equations with discontinuous right hand side, examples.
[9-12] Second order linear equations, boundary value problems, Green's function, existence and uniqueness of solution. The Sturm-Liouville problem, orthogonal systems, elements of the Fourier analysis, examples.

Enrollment :
Passed : Differential calculus of functions of several variables

Mandatory course - Regular study - Mathematics