School of Mathematics and Computing Sciences, Chalmers University of Technology and Goteborg University


TMA372/MAN660 Partial Differential Equations TM, 5p, Fall 2001


Check the Course diary! course diary.

General information:(Also available as ps.file and pdf.file)

This is the first course on partial differential equations (PDE) in Engineering Mathematics program (Teknisk matematik), and International Master Program in Mathematics, at Chalmers. It is also considered for the students of Electrical Engineering (E3) at Chalmers as well as GU students. Of course students who are not following these programs are also welcome. The course consists of 35 lecture hourse, 21 exercise hourse and gives 5 points.
Students of engineering programs: F, Kf and Kb cannot take this course.


Teachers:

Mohammad Asadzadeh (Lectures/Exercises)
telephone: 7723517
e-mail:mohammad@math.chalmers.se
URL:http://www.math.chalmers.se/~mohammad
Matematiskt Centrum, Eklandagatan 86, room 2331

Yan Yubin (Exercises)
telefon: 772 35 83
e-mail:yubin@math.chalmers.se
URL:http://www.math.chalmers.se/~yubin
Matematiskt Centrum, Eklandagatan 86, room 2328


Where and when: We meet in EL42

Tuesdays, 13.15-17:00 and Fridays, 8.00-11.45.

Tuesdays: Lectures 13.15-16, and time for questions 16.15-17.00,
Fridays: Lectures 8.00-9.45, and Exercises 10.00-11.45.


Literature:

K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Computational Differential Equations, Studentliterature 1996 (available at the Cremona book shop).


Home Assignments (Voluntary):

During the course two sets of assignments will be handed out. Each set will be divided in two parts. One part contains problems of the same type as on the final exam, but more complex and time consuming, the other part consists of computer exercises. You will account for your work by handing in the solutions to the problems and a short report on the computer work done. The home assignments can give a maximum of 12 bonus points on the final exam, where the computer exercises give 0-4 points each and the problems give 0-2 points each.


$\circ$ Assignment 1a (ps file) , Assignment 1a (pdf file) (handed in no later than week 5).

$\circ$ Assignment 1b (handed in no later than week 5).

$\circ$ Assignment 2a (ps file), Assignment 2a (pdf file) (handed in no later than week7).

$\circ$ Assignment 2b (handed in no later than week7).


The computer assignments:

The computer assignments use Matlab as the main tool. You can sit at MC if you want to (Yubin can give you a log-in name), but as long as you have access to Matlab 5.2 you can sit anywhere.

Apart from the two bonus generating assignments, we have also made some preparatory exercises, assignment 0. They deal with interpolation (ch 5 in the book) and multidimensional calculus (ch 13). Take a look at them to see if you can learn something from them, probably you will.

Assignment 0 (voluntary)
Assignment1b ((bonus generating ) (introduced in home assignments above)
Assignment2b(bonus generating)


Old exams with solutions:

Here are two examples of old exams, 98-12-15 (ps file) (pdf file) , 99-04-06 (ps file) (pdf file) , 99-12-14 (ps file) (pdf file) , 2000-04-25 (ps file) (pdf file) , 2000-12-13 (ps file) (pdf file) ,
with their solutions: solution to 98-12-15 (ps file) (pdf file) , solution to 99-04-06 (ps file) (pdf file) , solution to 99-12-14 (ps file) (pdf file) , solution to 2000-04-25 (ps file) (pdf file) , solution to 2000-12-13 (ps file) (pdf file) ,

Examples of two other old exams, with solutions, will be appear on the web-site during the course.


Final Exam (Compulsary):

The final exam is written and will contain both problems and theory questions. The grades on the exam will be:



$\circ$ 3: 20-29 points

$\circ$ 4: 30-39 points

$\circ$ 5: 40-50 points



The exam will be December 18, 14.15-19.15 in VV, no aids allowed. The corrected exams will be available in the reception room at Matematiskt Centrum which is open during lunch time, Monday to Friday, no later than three weeks after the exam.




Weekly program:

(Chapters in parantheses will be covered ''partially'' )

$\circ$ Week 1: Chapters (5), 6 and (7)

$\circ$ Week 2: Chapter 8

$\circ$ Week 3: Chapter 9

$\circ$ Week 4: Chapters 21, (10 and 13)

$\circ$ Week 5: Chapters 14 and 15

$\circ$ Week 6: Chapters 16 and 17

$\circ$ Week 7: Chapters 18 and (19)



Suggestions for exercises

(Some of these exercises will be demonstrated)

The even problems from Övningsexemple i PDE1 TM, (ps file), , (pdf file).

AND

Chapter 5: 5.11, 5.12, 5.17, 5.23, 5.27, 5.56

Chapter 6: 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, 8.3, 8.6, 8.7, 8.8, 8.11, 8.12, 8.15, 8.16, 8.18, 8.21, 8.22, 8.23, 8.32, 8.38, 8.41

Chapter 9: 9.4, 9.5, 9.7, 9.9, 9.10, 9.12, 9.13, 9.14, 9.19, 9.22, 9.23, 9.24, 9.26, 9.27, 9.28, 9.33, 9.43, 9.45, 9.46

Chapter 21: 21.1, 21.2, 21.3, 21.4, 21.5, 21.8, 21.9, 21.13

Chapter 14: 14.7, 14.10

Chapter 15: 15.5, 15.9, 15.11, 15.15, 15.20, 15.22, 15.24, 15.35, 15.39, 15.44, 15.45, 15.47

Chapter 16: 16.4, 16.7, 16.11, 16.14, 16.15, 16.18, 16.20

Chapter 17: 17.4, 17.8, 17.9, 17.10, 17.11, 17.13, 17.17, 17.18, 17.19, 17.20, 17.33

Chapter 18: 18.1, 18.3, 18.4, 18.5, 18.6, 18.9


What has changed so far:


$\circ$ I will emphasize 1D cases

$\circ$ An example note-book, Övningsexemple i PDE1, TM (ps file), and (pdf file), consisting of problems from some previous exams and solutions to the Lösningar för udda uppgifter i Övningsexemple i PDE1 TM (ps file), and (pdf file), odd problems in Övningsexemple i PDE1, are now available in the cousre homepage.

$\circ$ There is a course diary, describing the current process of lectures/ exercises.


Mohammad Asadzadeh
Nov. 7/2001