The discovery of solitons: reproduce the results of this classic paper by Zabusky and Kruskal. Make the best pictures you can - you have much better technology than they had!

Time-dependent schroedinger equation: reproduce these quantum-mechanical scattering experiments of a particle hitting a barrier. Make the best pictures you can - you have much better technology than they had!

Spontaneous spatio-temporal patterns in a chemical reaction: generate an interesting movie of a solution of this reaction-diffusion equation.

Homework #1 | due 11:59pm, Friday, Feb 12 | Solutions |

Homework #2 | due 11:59pm, Sunday, Feb 21 | Solutions |

Homework #3 | due 11:59pm, Friday, Feb 26 | Hints, Solutions |

Homework #4 | due 11:59pm, Friday, Mar 12 | Solutions |

Homework #5 | due 11:59pm, Friday, Mar 19 | Solutions |

Homework #6 | due 11:59pm, Friday, Mar 26 | Solutions |

Homework #7 | due 11:59pm, Sunday, April 4 | Solutions |

Homework #8 | due 11:59pm, Sunday, April 18 |

day | date | section | topics | pages | video | notebook |
---|---|---|---|---|---|---|

Day 1 | Feb 2 | 7.1 | ODE IVP, E/U | pages | video | |

Day 2 | Feb 4 | 7.1 | pages | video | ||

Day 3 | Feb 9 | 7.2 | Convergence of Euler's method. Single-step methods. | pages | video | ipynb |

Day 4 | Feb 11 | 7.3 | Order of accuracy of single-step methods. | pre, post | html, ipynb | |

Day 5 | Feb 16 | 7.3.4.1 | Taylor series method. Introduction to sympy. | pages | video | html, ipynb |

Day 6 | Feb 18 | 7.3.4.2-3, 7.4 | Runge-Kutta methods. Absolute stability. Adaptive error control. | pages | video | html, ipynb |

Day 7 | Feb 23 | 7.5-6 | Linear multistep formulas. | pages | video | html, ipynb |

Day 8 | Feb 25 | 7.5-6 | Absolute stability regions. | pages | videos: redone | html, ipynb |

Day 9 | Mar 2 | 7.5-7.7 | stability,consistency,convergence,implicit,stiffness | pre, post | video | html, ipynb |

Day 10 | Mar 4 | Exam 1 | (all of the above) | |||

Day 11 | Mar 9 | 10.1 | BVP for ODE, shooting | pages | video | html, ipynb |

Day 12 | Mar 11 | 10.1 | Variational equations, finite differences | pages | video | |

Day 13 | Mar 16 | 10.1 | SVD, error in finite differences, numpy subtleties,code for FD | pages | video | html1, ipynb1, html2, ipynb2 |

Day 14 | Mar 18 | 10.1 | Neumann BCs. Collocation | pages | video | html, ipynb |

Day 15 | Mar 23 | 10.1.3 | Galerkin method | pages | video (wrong mic, sorry) | html, ipynb |

Day 16 | Mar 25 | 10.1.3 | Galerkin method | pages | video | 1: html, ipynb, 2: html, ipynb |

Day 17 | Mar 30 | Ames | PDE, classification of quasilinear PDE | pages | video | |

Day 18 | Apr 1 | Parabolic (heat) eqn by finite differences | pages | video | ipynb, html | |

Day 19 | Apr 6 | BE, CN methods and eigenvalues | pages | video, errata | BE & CN: ipynb, html; eigenvalues: ipynb, html | |

Day 20 | April 8 | Exam 2 | BVP | |||

Day -8 | April 13 | Wave equation, FD stability | pages | video | Eigenvalues: ipynb, html; implementation: plain text | |

Day -7 | April 15 | Wave equation, instability, dispersion, elliptic PDE | pages | class, waves on water | heat eqn: wave_instability_demo.py, how dispersion manifests |