Course Diary TMA 372 and MAN 660, 2006

Final Exam with solutions: 061218 (pdf), 061218(ps)

Problem solving session:
December 13, 14.15-17 MV: H12

There will be no class on Tuesday November 21 and Monday December 11.

Office hours for assignment support: Thursdays 13:15-15, in MV:L2105.

Karin Kraft, kakr@math.chalmers.se

Study Guide:

Week 1: Chapters 5 and 6.
Week 2: Chapters (7) and 8.
Week 3: Chapter 9.
Week 4: Chapters 21 and 14.
Week 5: Chapter 15.
Week 6: Chapter 16.
Week 7: Chapter 17 (18).

Extra Support Material:

1. MATLAB Manual

2. PDE Lecture Notes 3. MATLAB Code Examples:

poisson.m, aposteriori.m, poi2D.m

Exercises:

Chapter 5: 5.12, 5.23, 5.27, 5.29

Chapter 6: 6.1, 6.2, 6.3, 6.11

Also,
1: Give a varitional formulation of -u''+u=f in (0,1), with u(0)=u(1)=0.

2: Write a FEM-formulation with piecewise linear, continuous functions, and a uniform stepsize h=1/4.

3: The same as above, but with piecewise quadratic functions.

Chapter 7: 7.3, 7.5, 7.24, 7.31 (prove in addition that there is exactly one minimum), 7.54

Chapter 8: 8.1, 8.6, 8.7, 8.8, 8.11, 8.12, 8.16, 8.18, 8.23

Chapter 9: 9.9, 9.12, 9.13, 9.19, 9.43, 9.45, 9.46

Chapter 21: 21.1, 21.2, 21.3, 21.4, 21.5, 21.8, 21.13

Chapter 14: 14.4, 14.7, 14.10, 14.21

Chapter 15: 15.5, 15.13, 15.15, 15.20, 15.22, 15.27, 15.39, 15.44, 15.47

Chapter 16: 16.7, 16.14, 16.15, 16.18, 16.20

Chapter 17: 17.8, 17.9, 17.10, 17.11, 17.13, 17.17, 17.33

Sample Exam Questions:

At least one question on the final exam will be to prove one of the following theorems.

  • Theorem 5.3: Prove the interpolation error estimate (5.12) for q=1 and p=infinity.

  • Show that the boundary value problem (8.2) is equivalent to (8.6) and (8.8).

  • Theorem 8.1: A priori error estimate for (8.2).

  • Theorem 8.2: A posteriori error estimate for (8.2).

  • Prove formulas (9.4), (9.5), and (9.6) for the initial value problem (9.3).

  • Theorem 21.1: Summarize the Lax-Milgram theorem (pp 513-515).

  • Theorem 15.1: A priori error estimate for the Poisson equation (15.18).

  • Theorem 15.3: A posteriori error estimate for the Poisson equation (15.18).

  • Lemma 16.1: 3 stability estimates for the heat equation (16.15).

    Ordinary Exam of 2005 with Solutions:

    Exam 2005-12-13 (pdf), (ps) , Solutions 2005-12-13 (pdf), (ps)

    Old Exams:

    2004-12-14 (pdf), (ps) , 2001-12-18 (pdf), 2002-12-17 (pdf), 2003-12-16 (pdf), 2004-04-13 (pdf)

    Solutions:

    2004-12-14 (pdf), (ps) , 2001-12-18 (pdf) , 2002-12-17 (pdf) , 2003-12-16 (pdf) , 2004-04-13 (pdf)

    Support material (mixed swedish and english) under construction :

    3. Exercises, and Solutions

    4. Problems, and Answers (to odd problems)


    • Editor: M. Asadzadeh
    Last modified: 2006-12-07