Advanced Mathematics III (Winter Semester 2010/11)
- Lecturer: PD Dr. Frank Hettlich
- Classes: Lecture (31006), Problem class (31007)
- Weekly hours: 2+4
- Audience: Mechanical Engeneering
| Schedule | ||
|---|---|---|
| Lecture: | Thursday 9:45-11:15 | ID SR Raum 203 |
| Problem class: | Monday 17:30-19:00 | Gerthsen-Hörsaal |
| Thursday 15:45-17:15 | ID SR Raum 202 | |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | PD Dr. Frank Hettlich | |
| Office hours: Wednesday 10:30am - 12am and on appointment | ||
| Room 1.042 Kollegiengebäude Mathematik (20.30) | ||
| Email: frank.hettlich@kit.edu | ||
Lecture & Problem Session
The new concept of an independent study course for Advanced Mathematics III (ID) will be introduced in the first lecture. Besides the review session on Thursday morning there will be a problem session on Thursday afternoon. Additionally we offer a Saaltutorium on Mondays from 17.30 to 19.00 Uhr in the Gerthsen lecture hall. During this tutorial course you may work on the problems of the current worksheet. Students and Coworkers will be there to help you and answer your questions.
Contents
- Differential Calculus in
- The Domain integral
- Vector Analysis
- Partial Differential Equations
- Fourier Analysis
- Introduction on Stochastics
The testat
If you successfully will attend the problem session, a testat will be given to you by the end of the semester, which is required for the application to the exam.
For the testat, you have to satisfy the following criteria:
- achieveing at least 150 points on the worksheets from 1 to 12. This is 25% of all the points you can get (each worksheet is 50 points worth)
- having at least 5 points on 10 of these worksheets.
Worksheets
Every week you will get a new worksheet with 5 problems. On any problem you can get up to 10 credit points.
| Worksheet | Date | Deadline | Topics |
| Worksheet 1 | 22.10.2010 | 28.10.2010 | Calculus in several varaiables, exact differential equations |
| Worksheet 2 | 29.10.2010 | 04.11.2010 | Integrating factor, implicitly defined functions |
| Worksheet 3 | 05.11.2010 | 11.11.2010 | extrem value problems, Lagrange multipliers |
| Worksheet 4 | 12.11.2010 | 18.11.2010 | iterated integrals, transformation formula |
| Worksheet 5 | 19.11.2010 | 25.11.2010 | curves, line integrals |
| Worksheet 6 | 26.11.2010 | 02.12.2010 | surfaces, surface integrals |
| Worksheet 7 | 03.12.2010 | 09.12.2010 | divergence theorem, Stokes theorem |
| Worksheet 8 | 10.12.2010 | 16.12.2010 | Stokes theorem, partial differential equations, method of characteristics |
| Worksheet 9 | 17.12.2010 | 13.01.2011 | partial differential equations, separation |
| Worksheet 10 | 14.01.2011 | 20.01.2011 | periodic functions, Fourier coefficients, orthogonal polynomials |
| Worksheet 11 | 21.01.2011 | 27.01.2011 | Fourier coefficients, Fourier series |
| Worksheet 12 | 28.01.2011 | 03.02.2011 | probability, Laplace experiments, conditional probability |
| Worksheet 13 | 04.02.2011 | 10.02.2011 | Bernoulli experiments, random variables, distribution functions |
Solutions to these problems (in German) will be available on the corresponding homepage of HM III
Maple Worksheets on AM I, II and III
A collection of Maple worksheets for the lectures AM I, II and III can be found at Worksheets-page (F. Hettlich).
Examination
The exam in Advanced Mathematics will take place in February/March.
In the exam the use of the following material is allowed:
- The AM I-III scriptum with handwritten notes.
- A printed formula book,
- an additional mathematical text book.
It is not allowed to use any electronical devices (caculator, etc.) and collections of old exams or other material.
References
Besides the scriptum we can recommend the following text books
- T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, K. Lichtenegger, H. Stachel: Mathematik. Spektrum Akademischer Verlag, Heidelberg, 2008 (in German).