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

# Advanced Mathematics I (Lecture) (Winter Semester 2015/16)

Lecturer: | PD Dr. Gudrun Thäter, Jonathan Rollin |
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Classes: | Lecture (0140000), Problem class (0150000) |

Weekly hours: | 4+2 |

#### NEWS

Exam Results |

Lecture: | Tuesday 14:00-15:30 | ID SR Raum 203 | Begin: 22.10.2015 |
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Thursday 9:45-11:15 | ID SR Raum 203 | ||

Problem class: | Monday 9:45-11:15 | SR 602 (Building 10.50) | Begin: 26.10.2015 |

Lecturer | PD Dr. Gudrun Thäter |
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Office hours: by appointment | |

Room 3.023 Kollegiengebäude Mathematik (20.30) | |

Email: gudrun.thaeter@kit.edu | |

Problem classes | Jonathan Rollin |

Office hours: whenever I am in my office | |

Room 1.039 Kollegiengebäude Mathematik (20.30) | |

Email: jonathan.rollin@kit.edu |

### Problem Sheets

A problem sheet will be published each Thursday on this webpage. Moreover printouts are available in the students office on Friday.

- Sheet No. 1 (sets, summation, binomial coefficients) : solutions sheet no. 1

- Sheet No. 2 (induction, complex numbers) : solutions sheet no. 2

- Sheet No. 3 (complex numbers, sequences) : solutions sheet no. 3

- Sheet No. 4 (sequences) : solutions sheet no. 4

- Sheet No. 5 (functions, inverse function, polynomials) : solutions sheet no. 5

- Sheet No. 6 (properties of sets, continuity, intermediate value theorem) : solutions sheet no. 6

- Sheet No. 7 (series, Leibniz' test, ratio test, root test, absolute convergence) : solutions sheet no. 7

- Sheet No. 8 (power series expansion, radius of convergence) : solutions sheet no. 8

- Sheet No. 9 (exponential functions, complex logarithm, trigonometric equations) : solutions sheet no. 9

- Sheet No. 10 (derivatives, mean value theorem) : solutions sheet no. 10

- Sheet No. 11 (L'Hospital, derivative of inverse function, Taylor series) : solutions sheet no. 11

- Sheet No. 12 (integration, differential equations) : solutions sheet no. 12

Students should solve the problems independently, after that they could discuss the solutions in groups. Only handwritten solutions will be accepted.

Please bring your solutions to the Problem Class on Monday, 9:45 am (11 days after the worksheet was published).

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.

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.

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

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.

### Examination

There is be a written exam on Saturday, **February 20, 9 - 11 AM.**

In order to take the exam it is necessary to obtain the testat (see above)!

Please note the information regarding the exam.

### 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

- 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