Numerical Analysis
1. Non-linear equations
Contraction principle, functional iterations
Newton's method in 1D
Functional iterations and Newton's method for system of equations
2. Interpolation and approximation of functions
Lagrange polynomials
Least squares and orthogonal polynomials
Trigonometric interpolation and approximation
3. Numerical integration
Newton-Cotes formulas
Gaussian quadrature
4. Numerical differentiation
Divided differences, forward dfferences
5. Solving ordinary differential equations (ODE)
Stability of ODE's
Convergence, consistency and 0-stability of ODE solvers
Implicit and explicit methods, forward and backward Euler
Introduction to Runge-Kutta methods.