Lecture plan/topics
This plan will be updated throughout the semester. Chapters refer to the book by Borthwick.
If you spot any mistakes in some of the notes below, please let us know, so that we can correct them.
| Day | Topic | Chapter | Assumed knowledge from other courses | |
|---|---|---|---|---|
| 23.8 | Introduction (selv study) | 1 | ||
| ODE theory and needed notation | 2.5-2.6 | |||
| Method of characteristics | 3.2 | |||
| 25.8 | Method of characteristics | 3.2-3.4, Notes H,Notes K | ||
| 30.8 | Method of characteristics | 3.2-3.4, Notes H, Notes K | ||
| Wave equation | 4.1-4-2 | Even and odd extensions of functions | ||
| 1.9 | Wave equation | 4.2-4.4 | ||
| 6.9 | Wave equation | 4.6 | double and triple integrals, surface integrals | |
| Vector calculus | 2.6 | |||
| 8.9 | Wave equation | 4.6-4.7 | ||
| 13.9 | Heat equation | 6.1-6.4 | 6.1: selv study | |
| 15.9 | Heat equation | 6.4, Notes H | ||
| 20.9 | Heat equation | Notes H | ||
| 22.9 | Laplace equation | 9.2, Notes H | ||
| 27.9 | Laplace equation | 9.2, Notes H | ||
| \(L^p\) spaces | 7.1-7.4, Notes K | 7.1: inner product space, normed vector spaces | ||
| 29.9 | \(L^p\) spaces | 7.1-7.4, Notes K | ||
| 4.10 | \(L^p\) spaces | 7.1-7.4, Notes K | ||
| Weak derivatives | 10.1 | |||
| 6.10 | Conservation laws | 10.2, Notes K | Green's theorem | |
| 11.10 | Conservation laws | 10.2, Notes K | ||
| Sobolev spaces | 10.3-10.4 | |||
| 13.10 | Weak solutions | 10.5-10.6 | ||
| 18.10 | Weak solutions | 10.5-10.6 | ||
| Poisson equation | 11.1-11.3, 11.8 | 11.8: selv study | ||
| 20.10 | Poisson equation | 11.1-11.3 | ||
| 25.10 | Poisson equation | 11.4, Notes K | Riesz representation theorem | |
| 27.10 | Poisson equation | 11.4, Notes K | ||
| Dirichlet eigenvalues | 11.5-11.7 | Eigenvalues and eigenvectors | ||
| 1.11 | Dirichlet eigenvalues | 11.5-11.7 | Orthonormal basis, Properties of Hilbert spaces | |
| 3.11 | Dirichlet eigenvalues | 11.5-11.7 | ||
| 8.11 | Distributions | 12.1-3, Notes K | [There are several common notations for distributions: \(u(\phi)\), \(\langle u,\phi\rangle\), and \((u,\phi)\). | |
| 10.11 | Distributions | 12.1-3, Notes K | ||
| Fundamental solutions | 12.4 | |||
| 15.11 | Fundamental solutions | 12.4 | ||
| Green's functions | 12.5 | |||
| 17.11 | Green's functions | 12.5 | ||
| Classification of linear PDEs | Chapter 4.4 | You must be inside the NTNU network, to have access. | ||
| 24.11 | Exam 2021 | Focus: The problems you are most intersted in. | ||