| Week 1 |
|
Preliminaries: Course intro, interpolation |
| Week 2 |
|
Details of Polynomial interpolation, splines |
| Week 3 |
|
Fourier series, discrete and Fast Fourier Transform |
| Week 4 |
|
Orthogonal polynomials (continuous least squares, min-max approx.) |
| Week 5 |
|
Derivatives and integrals (Newton-Cotes; composite) |
| | | |
| Week 6 |
|
Gaussian quadrature, Midterm (in class) |
| Week 7 |
|
ODE initial value problems, explicit one step methods |
| Week 8 |
|
Runge-Kutta methods, stiffness and absolute stability |
| Week 9 |
|
Implicit methods, multi-step methods |
| Week 10 |
|
Further topics in ODEs (systems, more on stability...) |
| | | |
| Week 11 |
|
Boundary value problems; simple shooting |
| Week 12 |
|
Finite differences for BVPs |
| Week 13 |
|
Method of lines for PDEs; finite differences for Poisson |
| Week 14 |
|
Finite differences for the heat equation; stability constraints |
| Week 15 |
|
Spectral methods for Poisson's equation (via FFT) |