# MAT-51316

Partial Differential Equations

spring 2011

## Teacher

prof. Robert
Piché

## Schedule

### Lectures

no lectures. The recorded lectures from last year (listed below) can be
used for self-study.
### Exercises

Tuesdays 2-4pm in Td308.
**No teaching Jan 25.**
### Midterm exam

Tuesday March 8 2011 in Td308
## Contents

The course covers the fundamental linear PDEs (transport, Laplace,
diffusion,
and wave
equation), how they arise as mathematical models of physical phenomena,
analytical tools (Fourier series, maximum principles,
Duhamel's principle, Green's functions, etc), and numerical solution
methods.
## Study Materials

Course notes

1. PDE models, transport
equation, method of characteristics slides,
recording,
exercises, solutions

2. One-dimensional models of
vibration, diffusion and heat conduction slides,
recording,
exercises, solutions

3. Wave equation: d'Alembert's
formula, energy analysis slides,
recording,
exercises, solutions

4. Diffusion initial-value
problem slides,
recording,
exercises,
solutions

5. Waves and Diffusion on
half-line, Duhamel's principle slides,
recording,
exercises, solutions

6. Separation of
Variables slides,
recording,
exercises,
solutions

7. Solving one-dimensional
problems with Matlab-PDEPE exercises,
solutions

8. Fourier series slides,
recording,
exercises,
solutions

9. Laplace's equation slides,
recording,
exercises,
solutions

10. Solving Laplace's
equation slides,
recording,
exercises,
solutions

11. Green's functions slides,
recording,
exercises,
solutions

12. Matlab PDE toolbox (demo)

vanhoja tentteja / old exams: 11.2008,
1.2009,
2.2010

vanhoja välikokeita / ole midterm exams: 1.2010

päivitetty / updated 18.1.2011 by
RP