Theorems on the iniquity and existence of solutions of ordinary differential equations; phase space; dependence on the parameters and initial conditions; linearization; critical points and their classification; stability theory; Lyapunov functions; geometric methods; Newton equation; solution of differential equations by means of power series; singular points and Frobenius method; boundary value problem; Green function; theory by Sturm-Liouville; Fourier series.

Standard basic courses of ordinary differential equations-1, linear algebra and infinitesimal calculus are sufficient for understanding the course.

The course homepage: http://www.tau.ac.il/~levant/applmath-1/index.html