Numerical Analysis

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.