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


TMA372/MAN660 Partial Differential Equations TM, E3, IM, and GU, 5p, Fall 2003


All new information will appear in the course diary continuously updated during the course.

Some information below is under reconsideration and will be updated soon.


Examination Dates!
December 16, 2003: 8.45-13.45 in V House
April 13, 2004: 8.45-13.45 in V House
General information: (Also will be available as ps.file and pdf.file).
This is the first course on partial differential equations (PDE) in Engineering Mathematics program (Teknisk matematik), International Master Program in Mathematics, and Electrical Engineering (E3) at Chalmers. It is also considered for GU students as well as for some PhD students at Chalmers that find the content of the course relevant for their studies. Of course students who are not following these programs are also welcome. The course consists of 35 lecture hours, 21 exercise hours and gives 5 points.
Students of engineering programs: Kf, Kb and K cannot take this course. Similarly engineering physics students that have taken the PDE course TMA690 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

Fredrik Bengzon (Exercises/Home- and Computer assignments)
telefon: 772 35 44
e-mail:bengzon@math.chalmers.se
URL:http://www.math.chalmers.se/~bengzon
Matematiskt Centrum, Eklandagatan 86, room 2255



Where and when: We meet/start in KB Tuesdays 28/10, 13.15-17:00

Lectures: Tuesdays 13.15-16.00 in KB and Fridays 8.00-9.45 in HA3

Exercises: Because of a schema collision we schedule one occasion of the excercises for the international master students on wednesdays 13.15-15.00 in ML10. Of course all other participants of the course are equally welcome to this exercise occasion as well.
Group 1: tuesdays 16.45-17.00 in KB.
Gruop 2: wednesdays 13.15-15.00 in ML10.
Whole class: Fridays 10-11.45 in HA3.


Literature:

K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Computational Differential Equations, Studentliterature (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 (ps file) , Assignment 1b (pdf file) (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).


Old exams with solutions:

Here are some 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) , 2001-12-18 (ps file) (pdf file) , 2002-12-17 (ps file) (pdf file) ,
2003-04-22 (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) , solution to 2001-12-18 (ps file) (pdf file) , solution to 2002-12-17 (ps file) (pdf file) , solution to 2003-04-22(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 in December (exact date and plce will be announced later). No aids are allowed.



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



$\circ$ I will emphasize one- and two-dimensional 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
November 07/2003