• Nonlinear systems: fixed point methods (contraction fixed point, monotonic fixed point, rate of convergence). Newton methods (variants of Newton’s method, incomplete Newton, secant method, quasi Newton …).
• Optimization: Definitions and review on differential calculus. Optimization without constraint. Algorithms for the optimization without constraint.
• Numerical solving of differential equations: Introduction. Generalities on the one step methods. The Runge-Kutta methods.
• Partial differential equations: One dimensional boundary value problems. Two dimensional elliptic problems.
• The Method of finite elements.