Research Group on Discrete Mathematics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.044

Institut für Algebra und Geometrie
Englerstr. 2
D-76131 Karlsruhe

Office hours:
Tu, Th, F 8:30-12:00

Tel.: +49 721 608 47412

Fax.: +49 721 608 46968

# Advanced Mathematics II (Summer Semester 2015)

 Lecturer: Prof. Dr. Maria Axenovich Lecture (0120010), Problem class (0) 4+2

This lecture is mandatory for students enrolled in the International program in Mechanical Engineering at the Carl-Benz School of Engineering.
The exam review will take place on Tuesday, 20.10.2015 1:15-3:00 p.m. in Benz Hörsaal

 Lecture: Problem class: Monday 9:45-11:15 ID SR Raum 203 Wednesday 8:00-9:30 ID SR Raum 203 Thursday 11:30-13:00 ID SR Raum 203
 Lecturer Prof. Dr. Maria Axenovich Office hours: Mon. 13:00-14:00 Room 1.043 Kollegiengebäude Mathematik (20.30) Email: maria.aksenovich@kit.edu M.Sc. Oleksandr Bondarenko Office hours: Dienstags von 15 bis 16 Uhr oder nach Absprache Room 1.049 Kollegiengebäude Mathematik (20.30) Email: bondarenko@kit.edu M.Sc. Thomas Rösch Office hours: Tuesday 14:00-15:00 Room 1.037 Kollegiengebäude Mathematik (20.30) Email: thomas.roesch@kit.edu

# Problem Sheets

A problem sheet will be published each Wednesday on this webpage. Moreover the printouts will be distributed at the ID.

Problem Sheet No. 1 (linear independence, basis, subspace, lines, planes)

Problem Sheet No. 2 (basis, dimension, normal form, distance, scalar product)

Problem Sheet No. 3 (normal form, distance, linear transformations, matrix product, rotation matrix)

Problem Sheet No. 4 (rotation/reflection/projection matrix, linear systems, dimension formula)

Problem Sheet No. 5 (cross product, determinant)

Problem Sheet No. 6 (eigenvalues, eigenspaces, diagonalization, first order differential equations)

Problem Sheet No. 7 (differential equations: Bernoulli, homogeneuous linear second/higher order, initial value problems)

Problem Sheet No. 8 (differential equations: Euler, systems; fundamental solution, Wronskian)

Problem Sheet No. 9 (differential equations: particular solutions (method of undetermined coefficients, method of variation of parameters), power series method)

Problem Sheet No. 10 (power series method, Laplace transform)

Problem Sheet No. 11 (Laplace transform: differentiation in preimage and image space; applications to differential equations)

Problem Sheet No. 12 (Laplace transform: convolution theorem, Delta-distribution; partial derivatives, gradient, Jacobian, Hessian matrix)

Students should solve the problems independently, after that they could discuss the solutions in groups of two and could also submit one solution set per group. Only handwritten solutions will be accepted.

The solutions will be corrected and graded by the tutor (Dhruv Singhal). Your graded solutions are available during the tutorial.

For each problem sheet one can obtain 50 points (10 points per exercise). Please note the criteria for the testat in the section below!

# Tutorial

There is a student tutorial given by Dhruv Singhal, Wednesdays 17:30- 19:00.

In the tutorial you will practice solving the exercises and there is room for questions.

# The Testat

If you successfully work on the home work (problem sheets), a testat will be given to you at the end of the semester. This 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.

# References

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

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

• 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.