1. Introduction: basic notions, solution of DE, Cauchy problem, exitence and uniqueness of solution.
2. Solving methods of ordinary first-order DE: separation of variables, linear and Bernoulli DE, direction field and othogonal trajectories; special types of 1st order ODE.
3.Simple numerical methods: Picard approximation, Euler method.
4. Applications: kinematic equations, evolution an logistic models.
5. Linear ODE of higher order I - homogeneous equations: structure and properties of solution, equations with constant coefficients.
6. Linear ODE of higher order II: complete equation with constant coefficients, equation with special right side; selected applications: mechanical vibrations, electrical circuits.
7. Systems of DE: linear systems, homogeneous systems with constant coefficients.
8. Non-homogeneous linear systems: structure of solution, analytical methods for solving.
9. Phase-mapping of solution of homogeneous 2nd order system, introduction to the stability theory.
10. The backgrounds of partial DE: basic notions, method of characteristics for the 1st order PDE.
11. Second order PDE: typology, important equations in mathematical physics.
2. Solving methods of ordinary first-order DE: separation of variables, linear and Bernoulli DE, direction field and othogonal trajectories; special types of 1st order ODE.
3.Simple numerical methods: Picard approximation, Euler method.
4. Applications: kinematic equations, evolution an logistic models.
5. Linear ODE of higher order I - homogeneous equations: structure and properties of solution, equations with constant coefficients.
6. Linear ODE of higher order II: complete equation with constant coefficients, equation with special right side; selected applications: mechanical vibrations, electrical circuits.
7. Systems of DE: linear systems, homogeneous systems with constant coefficients.
8. Non-homogeneous linear systems: structure of solution, analytical methods for solving.
9. Phase-mapping of solution of homogeneous 2nd order system, introduction to the stability theory.
10. The backgrounds of partial DE: basic notions, method of characteristics for the 1st order PDE.
11. Second order PDE: typology, important equations in mathematical physics.