Adv. Numeric Analysis
- Course introduction, review of errors and numerical stability
- Convergence analysis and order of methods, practical examples
- Nonlinear equations: Newton and Quasi-Newton methods
- Polynomial interpolation and splines
- Cubic splines, Hermite interpolation, multidimensional interpolation
- Least squares approximation, orthogonal polynomials
- Advanced numerical integration: Gaussian and adaptive quadrature
- Numerical differentiation and error analysis
- Runge-Kutta and multistep methods for ODEs
- Numerical methods for PDEs: finite difference, finite element (intro)
- Selected topics