** Exam information **

**General information can be found on this webpage.**

- Prerequisite registration: until 12.07.2017
- Exam registration: 17.07.2017 - 24.07.2017
- Exam on
** 29.07.2017, 11:30-13:30**

To register for the exam, use the student portal. It is necessary to have achieved the requirements from the Advanced Mathematics II problem sessions to be able to sign up.

It is possible to cancel the registration online during the registration period. For later cancellations, please see the staff at the institute.

### Problem Sheets

A problem sheet will be published each Tuesday on this webpage.

- Sheet No. 1 (Gauss elimination, intersection of planes and lines, linear and affine subspaces) Lösungen
- Sheet No. 2 (Linear independence, bases) Lösungen
- Sheet No. 3 (Scalar product, distance of geometric objects) Lösungen
- Sheet No. 4 (Periodic functions, Fourier polynomial) Lösungen
- Sheet No. 5 (Fourier series, product of matrices, matrix representation of a linear mapping) Lösungen
- Sheet No. 6 (Matrix representation of reflections and rotations, Kernel and Rank of a matrix) Lösungen
- Sheet No. 7 (Determinant, eigenvalues and eigenvectors) Lösungen
- Sheet No. 8 (Eigenvalues, eigenvectors, their geometric interpretation, homogeneous linear DE with constant coefficients ) Lösungen
- Sheet No. 9 ( Fundamental systems of homogeneous differential equations, systems of differential equations, reduction of order, Euler differential equation ) Lösungen
- Sheet No. 10 ( Fundamental systems, Wronskian determinant, method of undetemined coefficients, variation of parameters ) Lösungen
- Sheet No. 11 ( Power series method, parametric and improper integrals ) Lösungen
- Sheet No. 12 ( Laplace transform and inverse Laplace transform, convolution, solving (systems of) differential equations using Laplace transform) Lösungen

Homeworks can be submitted in groups of 2. Solutions written with a pencil are not accepted.

You will have 10 days to solve the problems. The submission deadline is 2 pm sharp on the next Friday.

The solutions will be corrected and graded by the tutor (Ziyad Sheeba).

If you successfully work on the homework, a testat will be given to you at the end of the semester. Please note the criteria for the testat in the section below!

### Handouts

### Tutorial

There is a student tutorial given by Ziyad Sheeba on Fridays at 2 pm.

In the tutorial, you will practice solving exercises in an interactive manner. You can also ask your questions connected to Lectures or Problem Classes.

### The Testat

You can obtain the testat by getting enough points for your homework solutions. The testat is necessary for you to be admitted to the exam.

For the testat, you have to satisfy the following criterias:

- Obtain at least 125 points from the worksheets 1 to 10. This is the 25% of all the total points obtainable (each worksheet is worth 50 points).
- For at least 8 of the worksheets, have at least 5 points from each.

### Examination

There will be a written exam on Saturday, **29 July.**

The following additives are allowed in the exam:

- the HM-Skriptum including your notes but without any glued additional pages
- a formula book
- a mathematical text book

If the formula book or the text book do not have an ISBN number it is required to show it in advance to the examinant at least one day before the exam (please come to the office hours).

In particular, no calculator is allowed.

You are only allowed to take the exam if you obtained the testat (see above)!

### References

General information and some tools for practicing are available on this webpage (partly in German).

There will be lecture notes for this class, distributed by the ID.

Besides the lecture notes, we can recommend the following text books:

- K. F. Riley, M. P. Hobson, S. J. Bence:
*Mathematical Methods for Physics and Engineering*. Cambridge University Press. - K. F. Riley, M. P. Hobson:
*Foundation Mathematics for the Physical Sciences*. Cambridge University Press. - T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, K. Lichtenegger, H. Stachel:
*Mathematik.* Spektrum Akademischer Verlag, Heidelberg (in German). - J. Stewart:
*Calculus, Early Transcendentals.* Brooks/Cole Publishing Company. - K. Burg, H. Haf, F. Wille:
*Höhere Mathematik für Ingenieure.* Volumes I-III. Teubner Verlag, Stuttgart (in German). - E. Kreyszig:
*Advanced Engineering Mathematics.* John Wiley & Sons. - E.W. Swokowski, M. Olinick, D. Pence, J.A. Cole:
*Calculus.* PWS Publishing Company. Boston. - Mathematica demos from Prof. R. Martin homepage