TMA026 / MMA430 Partial differential equations - second course
This page contains the program of the course: lectures and exercise sessions. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Under files there are video lectures from 2020, covering the same material (except the last week since we do hyperbolic problems this year), and solutions to some exercises. There you can also find lecture notes and old exams.
Program
The schedule of the course is in TimeEdit.
Lectures
| Day | Sections | Content |
|---|---|---|
| 20/3 | A.1 | Functional analysis |
| 22/3 | A.2 | Sobolev spaces |
| 24/3 | 3.1-3.2,3.5,3.7 | Elliptic problems |
| 27/3 | Exercises: A.6, A.11, A.15 | |
| 29/3 | Exercises: 3.8, 3.9, 3.11 | |
| 12/4 | 5.1-5.3, 5.4-5.6 | FEM |
| 14/4 | Exercises: 5.3, 5.6, 5.11 | |
| 17/4 | notes | Adaptive algorithms |
| 19/4 | 6.1 | Eigenvalue problems |
| 21/4 | Exercises: 6.1, 6.3 | |
| 24/4 | 6.2 | FEM for eigenvalue problems |
| 28/4 | 8.2 | Parabolic problems: eigenfunction expansion |
| 3/5 | Exercises: 6.5, 8.6, 8.10, 8.16 | |
| 5/5 | 8.3 | Parabolic problems: variational formulation |
| 8/5 | 10.1-10.2 | FEM for parabolic problems, ex 10.1 |
| 10/5 | 11.2 | Hyperbolic problems 2nd order, ex 10.4 |
| 15/5 | 11.3-4 | Hyperbolic problems 1st order |
| 17/5 | 13.1 | FEM for hyperbolic problems |
| 22/5 | Exercises: 11.3, 11.5, 13.1 | |
| 24/5 | Repetition |
Recommended exercises
| Day | Exercises |
|---|---|
| 24/3 | A.7, A.9, A.16 |
| 31/3 | 3.10, 3.13 |
| 14/4 | 5.5, 5.7, 5.17 |
| 21/4 | 6.7 |
| 28/4 | 8.4, 8.5, 8.11 |
| 5/5 | 10.3, 10.5 |
| 12/5 | 11.7 |
| 19/5 | 13.3 |
One one the exam questions will be to state and prove one of the following theorems:
A.4, 3.6, 5.3, 5.4, 6.5, 6.7, 8.5, 8.6, 10.1, 11.5
Course summary:
| Date | Details | Due |
|---|---|---|