### Advanced Mathematics I (ID) (Winter Semester 2010/11)

- Lecturer: Dr. habil. Gregor Fels
- 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: | Tuesday 14:00-15:30 | ID SR 203 | Begin: 22.10.2010 |

Friday 9:45-11:15 | ID SR 203 | ||

Problem class: | Wednesday 14:00-15:30 | ID SR 203 | Begin: 27.10.2010 |

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

Lecturer | Dr. habil. Gregor Fels | |

Office hours: Di 11-12, in vorlesungsfreier Zeit nach Vereinbarung | ||

Room 4A-01 Allianz-Gebäude (05.20) | ||

Email: gregor.fels 'at' kit.edu | ||

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

Office hours: | ||

Room Kollegiengebäude Mathematik (20.30) | ||

Email: |

# 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 (Kai Becker kai.becker@student.kit.edu a student from a higher semester) discusses problems with you. This tutor will also correct your homework.

# FAQ

Here you can find a list of faqhm1@iag1|frequently asked questions in German.

# 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 from at least 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. Please hand in your homework into the AM1-box near seminar room Z1, building 01.85 (Fritz-Erler-Str. 1-3).

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

Sheet | Solutions | Test | Date | Due | Topics |

1st Sheet | Solution 1 | test101@iag1|T 1 | 26.10.10 | 4.11.10 | sets, summation sign, system of linear equations, binomial coefficients |

2nd Sheet | Solution 2 | test109@iag1|T 2 | 02.11.10 | 11.11.10 | methods of proof, complex numbers |

3rd Sheet | Solution 3 | test103@iag1|T 3 | 09.11.10 | 18.11.10 | sequences, convergence, limit computations |

4th Sheet | Solution 4 | test103@iag1|T 3 | 16.11.10 | 25.11.10 | recursively defined sequences, monotonicity criterion, accumulation points |

5th Sheet | Solution 5 | test104@iag1|T 4 test105@iag1|T 5 | 23.11.10 | 02.12.10 | functions, continuity |

6th Sheet | Solution 6 | test105@iag1|T 5 | 30.11.10 | 9.12.10 | continuity, intermediate value theorem |

7th Sheet | Solution 7 | test106@iag1|T 6 | 07.11.10 | 16.12.10 | series, criteria for convergence |

8th Sheet | Solution 8 | test107@iag1|T 7 test108@iag1|T 8 | 14.12.10 | 23.12.10 | power series |

9th Sheet | Solution 9 | test109@iag1|T 9 | 21.12.10 | 13.01.11 | logarithm, trigonometric functions, complex equations |

10th Sheet | Solution 10 | test110@iag1|T 10 | 11.01.11 | 20.01.11 | differential calculus of one real variable |

11th Sheet | Solution 11 | test111@iag1|T 11 | 18.01.11 | 27.01.11 | mean value theorem, l'Hospital, Taylor expansion |

12th Sheet | Solution 12 | test112@iag1|T 12 | 25.01.11 | 10.02.11 | integral calculus |

# 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.