Partial Differential Equations F3, 2002,
home, week 1, week 2, week 3, week 4, week 5, week 6, week 7

Lectures and examination:
Claes Johnson
tel: 772 3518, 031-204327 (home)
claes@math.chalmers.se
Chalmers Finite Element Center Eklandagatan 80.
Lectures Monday and Thursday 10.00-11.45 in Kollektorn.

Preparation for exam Oct 25 2002: PM inför Tentamen

NEW: Omtentamen: Tisdagen 14/1 2003 fm sal V.

GUEST LECTURE: Monday 23/9: Prof Anders Bondeson on Computational Electromagnetics,
or how to solve Maxwell's Equations.

Exercises:
Richard Bergström
tel. 772 5314
ribe@math.chalmers.se
Chalmers Finite Element Center Eklandagatan 80.
Exercise whole group: Wednesday 13-15 Kollektorn (except week 5: instead FL61, FL72)
Individual instruction: Wednesday 15-17 FL10.

Literature:
Eriksson, Estep, Hansbo and Johnson: Computational Differential Equations (CDE), Studentlitteratur/Cambridge, 1996. CDE in brief

Optional complementing literature:
Eriksson, Estep and Johnson: Applied Mathematics: Body and Soul Springer, 2003.
Selected chapters for download: What is Mathematics? Laplacian models, The Crash Model, The Solar System,
Lorenz and the Essence of Chaos, Fem in 1d, Fem in 23d, Navier-Stokes: quick and easy.

Presentation of Chalmers Finite Element Center (Overview of some Part Diff Eqns).

Content:

  1. Intro: Poisson, Conv-diffusion, Wave, Navier-Stokes
  2. Poisson's equation
  3. Heat equation
  4. Wave equation
  5. Convection-diffusion-reaction equation
  6. Maxwell's equations
  7. Schrödinger's equation
  8. Energy estimates
  9. Fundamental solutions
  10. Galerkin methods for discretization in time and space (finite element methods,
    see Femlab available on a Chalmers site licence under Matlab with info-order ).
  11. Navier-Stokes with DOLFIN
Suggested CDE-reading:
Chapter 13 (Calculus review), 14-20 (Part. Diff. Eqns), 8-11 (Ordinary Diff. Eqns background).

Chalmers organization model: One Department-One Differential Equation.

Modern Society: Automation of Production and Computation.

Lecture notes from 2001:
Download lecture notes.

Exercise material:
Download exercises with hints and solutions.
Download problems with hints and solutions.

Projects:
Project 1 Supporting code: MySvenssonSolver.m, MySvenssonSolver2.m, MySvenssonSolver3.m,
Svensson's formula: Laplacian models,
Project 2 Supporting code: MyPoissonSolver.m, MyHeatEqSolver.m, MyPLPoissonSolver.m, MyPLHeatEqSolver.m, MyPLWaveEqSolver.m,
In short: write your own Femlab
Project 3 (optional) Navier-Stokes with DOLFIN, or a project according to your own choice.

The projects are to be reported in written form (short). We suggest hand-in of Project 1 in week 4 and Project 2 in week 6, and expect hand-in before the exam.

Examination:
Written exam at the end of course, Friday Oct. 25 am (f"ormiddag) in V-building. The exam has 50 points. In addition you can get up to 5+5 points from Project 1 and 2, reported in written form (short). Passing with grade 3 requires 25 points (adding points from exam and projects), passing with grade 4 requires 34, and grade 5 requires 43. If you reach the grade 4 this way you can also add up to 5 points from Project 3, that you may design yourself after an ok from the examinator. The points from the projects fade away after Oct 25 according to the formula bpoO26 x max(1-t^2,0) where bpoO26 means bonus points of October 26, and t is time in years. In particular, the points are gone after one year.
Written exam 011026 with solutions
Individual exam results.
Written exam 020115 with solutions
Individual 020115 exam results.

Preliminary bonus points on projects.

/Claes

Last modified: Thu Oct 24 15:07:26 MET DST 2002