Homework | Day | Date | Lectures |
Out | Due | Nr | Topic | Reading |
1 | | Wed | 02/07 | 1 | Introduction | |
| | Fri | 02/09 | 2 | Ordinary differential equations | 6.2 |
| | Mon | 02/12 | 3 | Some scalar linear initial value problems | 6.1 |
| | Wed | 02/14 | 4 | Von Neumann stability analysis | 6.6 & 6.3 |
| | Fri | 02/16 | 5 | Finite difference methods for the one-way wave equation | 6.3 |
| | Tue | 02/20 | 6 | Modified equation | LeVeque 11.1 |
2 | 1 | Wed | 02/21 | 7 | Lax equivalence theorem | 6.3 |
| | Fri | 02/23 | 8 | Numerical error analysis & convection-diffusion problems | 6.3 & 6.6 |
| | Mon | 02/26 | 9 | Wave equation, leapfrog, staggered grids | 6.4 |
| | Wed | 02/28 | 10 | Nonlinear conservation laws: examples, method of characteristics | 6.8 |
| | Fri | 03/02 | 11 | Nonlinear conservation laws: weak solutions | 6.8 |
| | Mon | 03/05 | 12 | Nonlinear conservation laws: high resolution shock capturing | 6.8 |
| | Wed | 03/07 | 13 | Nonlinear conservation laws: finite volume & particle methods | 6.8 |
3 | 2 | Fri | 03/09 | 14 | Higher space dimensions | |
| | Mon | 03/12 | 15 | Systems of initial value problems | |
| | Wed | 03/14 | 16 | Level set method | 6.9 |
| | Fri | 03/16 | 17 | Navier-Stokes equation | Griebel |
| | Mon | 03/19 | 18 | Navier-Stokes equation | Griebel |
| | Wed | 03/21 | 19 | Sparse matrices in applications | 7.1 |
| 3 | Fri | 03/23 | 20 | Elimination with reordering | 7.1 |
| | 03/26-03/30 | Spring break |
4 | | Mon | 04/02 | 21 | ILU, preconditioning, iterative methods | 7.2 |
| | Wed | 04/04 | 22 | Iterative methods | 7.2 |
| | Fri | 04/06 | 23 | Multigrid methods | 7.3 |
| | Mon | 04/09 | 24 | Multigrid methods | 7.3 |
| | Wed | 04/11 | 25 | Krylov subspace methods | 7.4 |
| | Fri | 04/13 | 26 | Krylov subspace methods | 7.4 |
| | 04/16-04/17 | Patriot's vacation |
| 4 | Wed | 04/18 | 27 | Least squares problems | 8.1 |
5 | | Fri | 04/20 | 28 | Saddle point formulation & weighted least squares | 8.1 |
| | Mon | 04/23 | 29 | Duality & minimization with constraints | 8.1 |
| | Wed | 04/25 | 30 | Regularization | 8.2 |
| | Fri | 04/27 | 31 | Inverse problems | 8.2 |
| | Mon | 04/30 | 32 | Tychonov regularization & ill posed operators in function spaces | 8.2 |
| | Wed | 05/02 | 33 | Calculus of variations | 8.3 |
| 5 | Fri | 05/04 | 34 | Calculus of variations | 8.3 |
| | Mon | 05/07 | 35 | Saddle point Stokes problem | 8.5 |
| | Wed | 05/09 | 36 | Linear programming | 8.6 |
| | Fri | 05/11 | 37 | Linear programming | 8.6 |
| | Sat | 05/12 | | Project presentations | |
| | Mon | 05/14 | 38 | Project presentations | |
| | Wed | 05/16 | 39 | Project presentations | |