Ordinary differential equations I 1000-114aRRZa

Ordinary differential equations and their solutions (definition, examples).
Initial value problem. Equations of higher order. (1 lec)

Solution methods for scalar equations: with separable variables, linear
equations, Bernoulli eq., complete differentials. (2 lec).

Local existence and uniqueness. Picard-Lindelof theorem. Dependence on
parameters and ininial values. Prolongation of solutions. (2 lec)

Linear systems of first order. The space of solutions. Wronski
determinant and Liouville theorem. Systems with constant coefficients. Linear
equations of higher order. Harmonic oscilator (dumping and forcing). (4 lec)

Autonomous equations and flows. Phase space and phase curves. Phase curves for a
2 dimentional linear system. Pendulum. Liapunov stability of solutions.
Asymptotic stability. Logistic model. Lotka-Volterra model. (3 lec).

Mechanics of solar system, Kepler laws. (2 lec).