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.

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

Home Assignments:

Assignment 1: Do exercises 8.35, 18.6 a-c, and 9.12. Write a short yet detailed report, not exceeding ten pages, explaning your work before 2005-11-28. Use MATLAB to do the coding parts. Hints: For 8.35 you need to read chapter 8, particularly, section 4, but not chapter 7. Obviously, it is impossible to compare with Femlab 1d. A good starting point for problem 18.6 might be this Matlab code, which solves -u''=f, u(0)=u(1)=0 using cG(1). In 9.12 consider only the case a=4.

Assignment 2: Can be found here. Hand in a short report of your work before the final exam.

Sample Exam Questions:

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