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General |
PHYS312: Supplementary material and notes
Every weekend, I will post here the material to be covered during the coming week. The required pre-reading materials will be listed at least by Sun night (for the Tue class) and by Tue night (for the Thus class). I will also indicate the chapter/section where the relevant material is in the recommended textbook. If/when I will hand out extra notes, I will post a copy of them here as well.
Links to Maple files will also be posted here, when appropriate. To use, save the files and open with Maple (available on all phas student lab computers). Most of these (with minor modifications) were prepared by prof. Birger Bergersen, and I thank him for letting me use them. If you need more help with the tutorial, let me know specifically what is needed, and I will add examples of those commands.
Here you can find notes for Math 267, which covers some of the topics we discuss in this class (at a somewhat lower level, from what I can see). You may find these useful. If you find other sets of notes online, which you think may be useful to your colleagues, send me the link and I will post them here.
| Lecture | Date | Pre-reading | Textbook chapter, extra notes, other material | What was covered |
| 1 | Sept. 6 | Info on this webpage | get hmw 1 | Introductions; Overview of the course |
| 2 | Sept. 11 | Definitions | 0.1 and 0.2, all parts about 1st order ODEs | Review 1st order linear ODE |
| 3 | Sept. 13 | Definitions | 0.1 and 0.2, all parts about 2nd order ODEs get hmw 2 |
Review 2nd order linear ODEs |
| 4 | Sept. 18 | Dirac delta function | Green's functions | Green's functions for ODEs with initial conditions |
| 5 | Sept. 20 | return hmw 2; get hmw 3 | Green's functions cont'd | |
| 6 | Sept. 25 | Boundary conditions | Green's functions (complete file) | Green's functions for ODEs with boundary conditions |
| 7 | Sept. 27 | Definitions for Fourier series | return hmw 3; get hmw 4 1.1, 1.2, 1.10 |
Green's functions cont'd Fourier series |
| 8 | Oct. 2 | 1.3, 1.5, 1.6, 1.7 | Fourier series cont'd | |
| 9 | Oct. 4 | Fourier series Maple file: mini-tutorial Maple file: Fourier series return hmw 4; get hmw 5 |
Even and odd periodic extensions | |
| Supplementary material: Fourier transforms | We will not use these in this course, but you will definitely run into them sooner or later. | The file explains the link between Fourier transforms and Fourier series, and how to use Fourier transforms to solve simple ODEs | ||
| 10 | Oct. 9 | Read section 3.1 | Parts of 3.3 + 3.6 | D'Alambert's solution for 1D wave eq. on infinite chains |
| 11 | Oct. 11 | pg 219: Eqs 1-7 | return hmw 5; get hmw 6 | D'Alambert's solution cont'd 1D wave equation: separation of variables |
| 12 | Oct. 16 | go over calculations from last lecture | Maple file:1D waves on finite chains | Wave equation (cont'd) |
| 13 | Oct. 18 | Read Section 2.1 | return hmw 6; get hmw7 | 1D heat equation |
| 14 | Oct. 23 | 1D heat equation (cont'd) | ||
| 15 | Oct. 25 | return hmw 7; get hmw 8 | MIDTERM | |
| 16 | Oct. 30 | Read section 4.2 | 2D heat equation | Heat (and Poisson's) equation in a 2D rectangle |
| 17 | Nov. 1 | return hmw 8; get hmw 9 | 2D heat equation cont'd | |
| 18 | Nov. 6 | 2.6 | Heat equation with convective BC | |
| 19 | Nov. 8 | 2.7, 2.8 return hmw 9; get hmw 10 |
Sturm-Liouville equations | |
| 20 | Nov. 13 | Read first 1.2 pages of the posted write-up | Inhomogeneous PDEs | Inhomogeneous PDEs: Poisson's equation in 2D |
| 21 | Nov. 15 | 4.5 return hmw 10; get hmw 11 |
Inhomog. heat equation Polar coordinates |
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| 22 | Nov. 20 | 5.4, 5.5., 5.7 | Electric potential in a disk (cont'd) Circular drum | |
| 23 | Nov. 22 | return hmw 11; get hmw 12 | Bessel functions | |
| 24 | Nov. 27 | Review | ||
| 25 | Nov. 29 | return hmw 12 | Review and conclusions |
