Tentative Calendar for TMA4305
| Week | Chapter/Section | Subject | Remarks |
| 3 | 1.1a,b,c,d | 1st order PDE | We skip section 1.1e |
| 4 | 1.2 (all); 2.1a | |
In 2.1a we skip Example 2. |
| 5 | 2.1b; 2.2a,b,c | Higher order PDE: General principles | |
| 6 | 2.3a,b,c; | Weak solutions of linear PDEs
Distributions | |
| 7 | 2.3 d
3.1 a,d; 3.3a,b; 3.4:a,b,(c) |
Fundamental solutions
Wave equation, dispersive equations |
We skip p. 70
Homework: 3.4:c |
| 8 | 3.2:a,b,c,d,(e); |
Wave equation in 3D and 2D, Huygens principle | Peter Lindvist will
lecture. |
| 9 | 4.1 | Laplace equation | No lecture on monday |
| 10 | 4.1 d, 4.2 a | Laplace
equation | Section 4.2.f: skip Theorem 10. |
| 11 | 4.2 a - f, 4.3 a | Laplace
equation | |
| 12 | 4.3 a, b; 4.4
5.1 a |
Laplace equation
Heat equation | HW: Read Section
4.3.c
. |
| 13 | 5.1a,b, 5.2a,b,d,
5.3 a, b;
6.1 a, c, d
| Heat equation
Review of basic functional analysis
| In 5.2.d we skip Thm. 2.
In 5.3.a we
skip the proof
In 6.1 d we skip Thm. 2 and
Corollary |
| 14 | 6.1, parts of 6.3, 6.5
6.2 a, c, d
| Lp and Sobolev spaces
Weak
solutions of Dirichlet problem for elliptic
equations. Lax-Milgram Theorem
| |
| 15 | | | Easter
holidays |
| 16 |
6.2 d
Parts of 6.3
and 6.5
7.1 a-d | Proof of Lax-Milgram thm
Weak convergence and compactness
results
Variational
methods | |
| 17 | 7.1 a-d | Variational
methods | |
| 18 | 8.3 a-b
| Maximum principles
Exercises + Summary -
About Exam | No lectures on Thursday |
|
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