My favorite equation
\( \partial_t u=\mathcal{L} {u}+\mathcal{N} u \) The universe is written in the language of mathematics (Galileo) |
Class schedule by chapters/sections (tentative) | |||
---|---|---|---|
PDE from Physics (Chapter 1) | 1.1 - 1.3, 1.4*-1.5* | ||
Wave and diffusion equations (Chapter 2) | 2.1 - 2.3, 2.4* | ||
Reflections and sources (Chapter 3*) | 3.1-3.5* | ||
Exam 1 | Chap.1, 2 and 3* | ||
Separation of variables (Chapter 4) | 4.1-4.2,4.3*-4.4* | ||
Fourier series (Chapter 5) | 5.1-5.2, 5.3* | ||
Laplace equation (Chapter 6) | 6.1-6.2, 6.3** | ||
**Green's functions (Chapter 7**) | 7.1*, 7.2-7.3* | ||
Exam 2 | Chap.4, 5 and part of Chap.6* & 7* | ||
**Computations for PDE | 8.1**-8.2** | ||
Final Exam |
Review | Exam | Date |
---|---|---|
Review Exam I | Exam I | |
Review Exam II | Exam II | |
Review Exam III | Exam III | |
Review Final | Final Exam |
Reading-Tutorial | Reading/Tutorial | Chapter/Section |
---|---|---|
Reading I | Tutorial I | |
Reading II | Tutorial II | |
Reading III | Tutorial III | |
Reading IV | Tutorial IV |
Green's theorem (2d): $$\int_{\partial R}{\bf F}\cdot {\bf n} ds=\int_R\, \mathrm{div}\, {\bf F}\, dA$$
The divergence theorem in 3d (Gauss' theorem): \begin{align} &\int_{\partial\Omega}{\bf F}\cdot {\bf n} d\omega=\int_\Omega \mathrm{div} {\bf F} dV \end{align}