Theory of partial differential equations
Course 155010, academic year 2005/2006, semester 1. The course is part of the curriculum for the international Master of Applied Mathematics programme of the Department of Applied Mathematics at the University of Twente. Besides the lectures, exercise classes will be given by Chris Stolk, and Manfred Hammer. The course largely follows a schedule that was projected by Stephan van Gils, based on the book Beginning Partial Differential Equations by Peter V. O'Neil, John Wiley & Sons, 1999.
The weekly procedure consists of lectures (Monday afternoon, 15:45-17:25, room TE 4 (from week 48 on: RA Studio)) and exercise classes (Wednesday afternoon, 15:45-17:25, two groups, rooms TE 7, TE 6), from week 46, November 14, 2005, till week 03, January 18, 2006. The course closes with a written examination in week 05, 2006, Wednesday morning, February 01, 09:00-12:00 in room SP 1.
The table shows the prospective schedule of the course:
week | lecture | classroom exercises | homework | deadline | bonus |
46 | 1.1-1.4 | exercises week 46 | homework part I | ||
47 | 2.1-2.4 | exercises week 47 | |||
48 | 2.5-2.8 | exercises week 48 | homework part II | 28.11.05, 15:45, part I | 3 |
49 | 4.1-4.4, 4.7 | exercises week 49 | |||
50 | 4.9-4.11, 5.1+5.2 | exercises week 50 | homework part III | 12.12.05, 15:45, part II | 3 |
51 | 5.3-5.5 | exercises week 51 | |||
02 | 6.1-6.6 | exercises week 02 | homework part IV | 09.01.06, 15:45, part III | 3 |
03 | 6.7-6.9, 6.11-6.14 | exercises week 03 | 18.01.06, 15:45, part IV | 3 |
The numbers indicate sections in the book of P. V. O'Neil, which (roughly) will be the subject of the lectures. The contents may change, depending on the progress of the course.
The lectures are accompanied by regular classroom and homework exercises. Sheets with the problems (probably partly from the textbook) will be handed out at the beginning of the exercise classes, or at the end of the lecture, respectively. A few days in advance the files will also be linked to the corresponding entry in the table above. A collection of example solutions exists for some of the classroom exercises of previous years (numbers refer to exercises in the textbook).
Homework exercises are scheduled for each two weeks. The solutions are to be delivered (on paper, electronic submissions are not accepted!) at the beginning of the lecture two weeks after the problems have been handed out. Although it is not strictly compulsory, participation in the homework scheme is highly recommended to stimulate a continuous working attitude. While a discussion on the topics of the homework is encouraged, the problems are to be solved and to be written down individually. For correct solutions you will be rewarded by three bonus points for each part of problems, which sum up to a maximum of 12 points. These lessen the burden of the final examination: Provided you have earned at least eight bonus points b, your mark m for this course will be determined according to the expression m = 1+b/4+(p/4)(9-b/4)/9, where p is your score (in a range between 0 and 36) in the final examination.
For the homework exercises, the use of a computer algebra program such as Maple or Mathematica is encouraged. This concerns e.g. the computation of partial derivatives, the solution of ordinary differential equations, or the analytic solution of small systems of algebraic equations.
(31.03.2006)