Department of Mathematical Sciences,
Chalmers University of Technology
and
Göteborg University
#### TMA026 Partial differential equations, advanced course, period 1,
2006, 5 points

(Kurskod på GU: MAN665.)

This course is a continuation of TMA372 (TMA690) Partial Differential
Equations and treats more deeply the theory of elliptic, parabolic,
and hyperbolic partial differential equations, as well as numerical
methods and applications in engineering and physics.

The course is suitable for students in the TM programme of
Chalmers, undergraduate students in mathematics of the Göteborg
University, and graduate students in applied subjects at Chalmers.

**Contents**

Existence and regularity of solutions of linear ordinary differential
equations and linear elliptic, parabolic and hyperbolic partial
differential equations. The maximum principle. Finite element and
finite difference methods. Error estimates. Applications to heat
conduction, wave propagation, convection-diffusion, reaction-diffusion,
neutron transport.

**Preparations**

It is recommended that the students have taken
TMA372
(or
TMA690)
Partial Differential Equations and
TMA401
Functional Analysis,
but this is not absolutely necessary.

**Literature**

S. Larsson and V. Thomée,
Partial Differential Equations with Numerical
Methods,

Texts in Applied Mathematics 45, Springer, 2003.
Cover,
contents,
corrections (ps).

The book is available at the Cremona bookshop.

Note: the Cremona bookshop has made some mistake and they don't have
the book. I suggest that you order it from some internet bookshop
instead. In the meantime I give you the first chapters here.

**Examination**

The examination is based on homework assignments and a written exam at
a date to be decided.

Written exam: Tuesday October 24, e V (14.00-18.00 in the V-building)

Here is a plan of the lectures and
exercises.

Here is the list of
scores from the hand-in problems.

**The exam has been graded!** Here is the result.

**Teacher**

Stig Larsson

**Schedule**

Monday 13.15-15.00 in room MV:H11

Wednesday 8.00-9.45 in room MV:H11

The course begins on Monday, September 4, 2006.

Welcome!
/stig