TMA025 Partial differential equations, advanced course, period 1, 2000

(Obs: Kursen ersättes av TMA026 från och med 2001-02 på grund av poänghöjning. Kurskod på GU: MAN665)

Obs: I Chalmers kurskatalog 2000 står det att denna kurs inte ges i år. Men på begäran kommer den ändå att ges som självstudiekurs.

This course is a continuation of TMA371 (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 TMA371 (or TMA690) Partial Differential Equations and TMA400 Functional Analysis, but this is not absolutely necessary.

Literature
Partial Differential Equations with Numerical Methods, lecture notes by V. Thomée and S. Larsson (distributed in class).

Teacher
Stig Larsson
telephone: 772 35 43, 45 46 93
e-mail: stig@math.chalmers.se
URL: http://www.math.chalmers.se/~stig
Matematiskt Centrum, Eklandagatan 86, room 2329

Teaching
The course will be based on student activity. There will only be a few lectures or exercises. Instead we will meet once a week for supervision of homework assignments and discussion of theory.

Examination
The examination will be based on weekly homework assignments, student activity in the weekly classes, and a final oral exam.

Study questions

Weekly assigments

Schedule
The students are divided into three groups who meet me in my office one hour per week. In addition I will give one hour lecture per week.

Lecture: Mondays 10.00-10.45 in seminar room S1 (room 1305),
except Oct 10 when we meet in group room G5 (room 2340).

Group 1: Thursdays 9.00-10
Group 2: Mondays 10.00-11
Group 3: Tuesdays 15.15-16

Introductory meeting
Monday August 28, 10.00, in seminar room S4, Mathematics Center.
This will be a short meeting to decide about the schedule and other things.

Welcome! /stig