### Advanced Mathematics III (Winter Semester 2010/11)

• Lecturer:
• 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).