### Advanced Mathematics I (ID) (Winter Semester 2009/10)

- Lecturer: PD Dr. Tilo Arens
- Classes: Lecture (31004), Problem class (31005)
- Weekly hours: 4+2
- Audience: Mechanical Engeneering (from 1. semester)

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

Schedule | |||
---|---|---|---|

Lecture: | Friday 9:45-11:15 | Begin: 23.10.2009 | |

Tuesday 14:00-15:30 | |||

Problem class: | Wednesday 14:00-15:30 | Begin: 28.10.2009 |

Lecturers | ||
---|---|---|

Lecturer | PD Dr. Tilo Arens | |

Office hours: Wednesday 11:00-12:00 Uhr | ||

Room 1.047 Kollegiengebäude Mathematik (20.30) | ||

Email: tilo.arens@kit.edu | ||

Problem classes | Dr. Andreas Helfrich-Schkarbanenko Dr. | |

Office hours: | ||

Room Kollegiengebäude Mathematik (20.30) | ||

Email: | ||

Problem classes | Dr. Sven Heumann | |

Office hours: Mittwoch, 15:00 - 16:30 Uhr und nach Vereinbarung | ||

Room 4C-02 Allianz-Gebäude (05.20) | ||

Email: sven.heumann@kit.edu |

# Lecture & Problem Session

This course includes three different components:

- In the lectures you learn about new topics. For this part of the course there exist bilingual lecture notes which you may also use during the exam. The lecture notes will be handed in the first session of the lectures.
- In the problem sessions, examples corresponding to the topics of the last week's lectures will be demonstrated. With the aid of these examples, it should be possible for you to complete the weekly homework assignments.
- Additionally we offer a tutorial, where a tutor (a student from a higher semester) discusses problems with you. This tutor will also correct your homework.

# The testat

If you successfully work on the home work, a testat will be given to you at the end of the semester, which is required for registration for 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:

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

# Worksheets

Every week, a new worksheet will be handed out with 5 problems. On any problem you can get up to 10 points. Your solutions must be handed in by the next week.

During the semester you will find more information on problems here.

Sheet | Solutions | Date | Due | Topics |

1st sheet | no longer available | 27.10.09 | 5.11.09 | sets, summation sign, system of linear equations, binomial coefficients |

2nd sheet | no longer available | 3.11.09 | 12.11.09 | methods of proof, complex numbers |

3rd sheet, 2nd version | no longer available | 10.11.09 | 19.11.09 | sequences, convergence, limit computations |

4th sheet | no longer available | 17.11.09 | 26.11.09 | recursively defined sequences, monotonicity criterion, accumulation points |

5th sheet | no longer available | 24.11.09 | 3.12.09 | functions |

6th sheet | no longer available | 1.12.09 | 10.12.09 | continuity, special properties of real-valued functions |

7th sheet | no longer available | 8.12.09 | 17.12.09 | series, criteria for convergence |

8th sheet | no longer available | 15.12.09 | 7.1.10 | Cauchy product, Power series, Euler's formula |

9th sheet | no longer available | 22.12.09 | 14.1.10 | logarithm, trigonometric functions, complex equations |

10th sheet | no longer available | 12.1.10 | 21.1.10 | differential calculus of one real variable |

11th sheet | no longer available | 19.1.10 | 28.1.10 | extreme value problems, Taylor series |

12th sheet | no longer available | 26.1.10 | 4.2.10 | integral calculus |

# Additional material

# Maple - Worksheets

In addition to the Advanced Mathematics lectures there are Maple Worksheets available. You can download each worksheet as ".mw" files and work on it on your computer.

# Examination

The examinations in Advanced Mathematics will take place in February/March. During the exam the use of the following material is allowed:

- The AM I lecture notes including any handwritten notes in your copy.
- A printed book of formulae,
- and additionally any one 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 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.