This lecture is mandatory for students enrolled in the International program in Mechanical Engineering at the Carl-Benz School of Engineering.

Please note: The AM I exam is part of the *Orientierungsprüfung*, which you must complete by the end of the third semester.

### Midterm

### Problem Sheets

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

- Problem Sheet No. 1 (sets, finite sums, induction)
- Problem Sheet No. 2 (absolute value, induction, complex numbers, quadratic equations)
- Problem Sheet No. 3 (polar coordinates, quadratic equations, limits of sequences)
- Problem Sheet No. 4 (recursive sequences, complex sequences, polynomials, functions)
- Problem Sheet No. 5 (inverse function, continuity, sets)
- Problem Sheet No. 6 (intermediate value theorem, maximum and minimum, series)
- Problem Sheet No. 7 (ratio test, root test, comparison test, Leibniz test)
- Problem Sheet No. 8 (power series, radius of convergence, trigonometric functions)
- Problem Sheet No. 9 (power series expansion, trigonometric equations, Euler's formula)
- Problem Sheet No. 10 (logarithm, derivatives)
- Problem Sheet No. 11 (extremal value problems, L'Hospital, Taylor series)
- Problem Sheet No. 12 (integrals, differential equations)

Students should solve the problems and write down solutions independently and also should discuss the solutions in groups. Please submit written solutions in the beginning of the problem class, that is, by **Tuesday, 15:45 AM** (12 day later).

Only handwritten solutions will be accepted. Please do not use a pencil! The solutions will be corrected and graded by the tutor (Abdallah Alshanawani). Your graded solutions are available during the tutorial. Please grab them there!

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

### 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 criteria:

- Obtain at least 125 points on worksheets 1 to 10. This is 25% of all the total points obtainable (each worksheet is worth 50 points).
- For at least 8 of those worksheets have at least 5 points from each.
- Pass the
**midterm test** on Monday December 11 (in the lecture).

### Exercises from Problem Class

### Tutorial

There is a student tutorial given by Abdallah Alshanawani. In the tutorial you will practice solving exercises in an interactive manner. You can also ask your questions connected to lectures or problem classes.

### Examination

There will be a written exam on

- Friday,
**February 23**, **8:00 - 10:00**, - in
**Nusselt Lecture Hall** (building 10.23, see on map).

- The exam will be
**closed book**, the only material allowed is one handwritten page of notes.

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.