1. Systems of ODE -- basic examples and applications.

2. Existence, uniqueness and further properties of solutions.

3. Systems of linear equations, variation of constants, matrix exponential.

4. Asymptotic behavior, stability.

Existence, uniqueness, basic properties of solutions to ODE's. Solution methods to selected ODE's.

Qualitative analysis. Applications: derivation and analysis of basic models (biology, physics, economy).