| Lecture 1: | Introduction. Discussion of projects and hand-out of list of exercises. A first numerical example: Why does not the atmosphere fall down? The Euler Method. G&N chap. 1. |
| Lecture 2: | Ordinary differential equations - initial value problems.
Projectile motion: Who wants
to be a rocket scientist?
Estimating errors. Richardson extrapolation.
Improvements of the Euler method: Runge-Kutta algorithms. G&N chap. 2 and appendix A. |
| Lecture 3: | Ordinary differential equations - initial value problems. Why are physicists so fond of harmonic springs? Stability analysis. The Euler-Cromer method and other algorithms. Discrete and Fast Fourier Transforms. G&N chap. 3 and appendix C. |
| Lecture 4: | Ordinary differential equations - boundary value problems. How do I keep my beer cold on a hot summer's day? The shooting method and introduction to matrix diagonalization. Numerical integration. G&N chap. 10.1-10.3, appendix E and H. |
| Lecture 5: | Partial differential equations. Introduction and simulation examples, general techniques for solving PDEs numerically. Introduction to the PDE project. How to cook an egg or a ham... G&N chap. 5, 6 and 7.4. |
| Lecture 6: | Partial differential equations - the diffusion equation. Finite difference scheme. Explicit Euler, implicit Euler, Crank-Nicolson. von Neumann stability analysis. G&N chap 7.4. |
| Lecture 7: | Partial differential equations - static problems. Laplace and Poisson equations. Relaxation methods. Jacobi method, Gauss-Seidel method, successive overrelaxation (SOR) method, fourier transform method. G&N chap 5. |
| Lecture 8: | Partial differential equations - waves. Euler method, Lax method, leapfrog method. Schrodinger equation. G&N chap 6. |
| Lecture 9: | Random walks and stochastic processes. Where is that drunkard? Introduction to project 3. Random walks. Random numbers. Probability distributions. The central limit theorem. First-passage time densities. G&N chap. 7 and appendix F, G. |
| Lecture 10: | Random walks and stochastic processes. Transforming random numbers: the (discrete and continuous) transformation method, the accept/reject method. Anomalous random walks. Reaction-diffusion. G&N chap. 7 and appendix F, G. |
| Lectures 11-12: | Optimization. G&N appendix B |
| Lecture 13: | Monte Carlo methods. Monte Carlo integration. Simulated annealing, global optimization. Introduction to HP-model project. G&N chap. 8 |