Course Diary TMA 372 and MMG800, 2013


Latest news
2013: Ordinary Exam AND Solutions: tenta_2013-03-13(pdf),

Note: We have no PDE cclass on jan 24: There will not be Lecture/Exercise on jan 24.

Answers to some exercises in CDE (pdf),

  • Lecture Notes, FEM_Version4 (NEW): (chapters 2 3 and 5-12 are relevant to our course), (pdf).
  • Ordinary Exam of 2011 with Solutions: Exam 2011-03-14 (pdf),
  • Ordinary Exam of 2010 with Solutions: Exam 2010-03-08 (pdf),

  • Please do not! submit your solutions by e-mail.

    • Study Guide:

    Extra Support Material:

    1. MATLAB Manual

    2. PDE Lecture Notes (Do not print! this is old version that follows the "Black Book")

    3. MATLAB Code Examples: poisson.m, poi2D.m

    Useful to 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).
    As for the proof of Lax-Milgram theorem, you may use the proof of Theorem 32 in my lecture notes on web-site, pp 177-179.

  • 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). (cancelled)

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

    Exams and Solutions:


    2012-08-29 (pdf), 2011-08-24(pdf), 2011-06-04(pdf), 2011-03-14(pdf), 2010-03-08(pdf), 2010-01-12(pdf),
    2009-08-26(pdf), 2009-03-09(pdf), 2009-01-13(pdf), 2008-03-10 (pdf), 2006-12-18 (pdf),

    Old Exams:
    2005-12-13 (pdf), 2004-12-14 (pdf), 2001-12-18 (pdf); 2002-12-17 (pdf); 2003-12-16 (pdf); 2004-04-13 (pdf)

    Solutions:
    2005-12-13 (pdf), 2004-12-14 (pdf), 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: 2012-01-12