Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation. Numerical solution of ordinary differential equations. Iterative solution of linear systems. Computation of least squares approximations. Discrete Fourier approximation and the fast Fourier transform. Matlab programming.
| Homework # | Topics |
|---|---|
| Homework 1 | Euler's method and error analysis |
| Homework 2 | Taylor's method, Midpoint method. Order of convergence and error analysis |
| Homework 3 | Euler's method, Runge-Kutta method of order 4, Adams 4th order predictor-corrector method, Milne-Simpson predictor-corrector method. Error analysis and stability. |
| Homework 4 | Newton's method, Steepest Gradient Descent, Homotopy continuation method with midpoint method and Runge-Kutta method of order 4. Order of convergence. |