– Definition of an autonomous ODE, definition of a Cauchy Problem, Theorem of Cauchy-Lipschitz
– Definition of a maximal solution and the maximum domain, analysis of the stability
– Qualitative properties: conservative systems, Lyapunov functions, introduction to bifurcations (+ limit cycles)
– Construction of the phase portrait of an ODE in dimension 1 and 2
– Numerical integration of an autonomous ODE (Euler, RK, Crank-Nicholson)
– Analysis of a numerical scheme: stability, consistency and convergence
The above-mentioned concepts will be introduced and applied to 4 dynamical systems used all along this class
