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

# ++++ Examination for Advanced Mathematics 1 ++++

Please use the following link to find out, where your rooms and seats are during the examination: List of seats/rooms .

In the first column of the list you can find your matriculation number, then in the same row and the next column your room and in the last column your seat number. There is also some campus plan on this site, where you can find the rooms/lecture halls.

Please make sure that you are at your seat at least 10 minutes before the examination begins.

There are a few advices concerning the exam, which you can find on this site: Examination details .

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# Lecture & Problem Session

This course includes three different components:

- During the lectures you learn about new topics. For this part of the course there are lecture notes which you may also use during the exam. The lecture notes will be distributed by the International Department (ID).

The first lecture is on October, 20th, 2011.

- During the problem sessions, examples corresponding to the topics of the last week's lectures will be demonstrated. With the aid of these examples, you should be able to complete the weekly homework assignments.

The problem class starts on October, 26th, 2011.

- Additionally we offer a tutorial, where a tutor (Kai Becker kai.becker@student.kit.edu a fellow senior student) discusses problems with you. This tutor will also correct your homework.

The tutorial starts the second week of classes.

# 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. Additionally we offer some *tests* where you can check your knowledge.

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

Sheet 1 | loesungen1.pdf@hm1mach2011w@iag1|Solution 1 | test101@iag1|T 1 | 10-24-2011 | 10-31-2011 | Sets, summation sign, system of linear equations, binomial coefficients. |

Sheet 2 | loesungen2.pdf@hm1mach2011w@iag1|Solution 2 | | 10-31-2011 | 11-07-2011 | Induction, complex numbers. |

Sheet 3 | loesungen3.pdf@hm1mach2011w@iag1|Solution 3 | test102@iag1|T 2 , test103@iag1|T 3 | 11-07-2011 | 11-14-2011 | Complex numbers, sequences. |

Sheet 4 | loesungen4.pdf@hm1mach2011w@iag1|Solution 4 | test102@iag1|T 2 , test103@iag1|T 3 | 11-14-2011 | 11-21-2011 | Convergence, limits. |

Sheet 5 | loesungen5.pdf@hm1mach2011w@iag1|Solution 5 | test104@iag1|T 4 | 11-21-2011 | 11-28-2011 | Polynomials, functions, inverse function. |

Sheet 6 | loesungen6.pdf@hm1mach2011w@iag1|Solution 6 | test104@iag1|T 4 , test105@iag1|T 5 | 11-28-2011 | 12-05-2011 | Continuous functions, intermediate value theorem, series. |

Sheet 7 | loesungen7.pdf@hm1mach2011w@iag1|Solution 7 | test106@iag1|T 6 , test107@iag1|T 7 | 12-05-2011 | 12-12-2011 | Convergence tests, power series. |

Sheet 8 | loesungen8.pdf@hm1mach2011w@iag1|Solution 8 | test108@iag1|T 8 , test109@iag1|T 9 | 12-12-2011 | 12-19-2011 | Power series, elementary functions for complex arguments. |

Sheet 9 | loesungen9.pdf@hm1mach2011w@iag1|Solution 9 | test110@iag1|T 10 | 12-19-2011 | 01-16-2012 | Complex equations, differential calculus of one real variable |

Sheet 10 | loesungen10.pdf@hm1mach2011w@iag1|Solution 10 | test110@iag1|T 10 , test111@iag1|T 11 | 01-09-2012 | 01-16-2012 | Extreme value problems, mean value theorem, de l'Hospital's rule |

Sheet 11 | loesungen11.pdf@hm1mach2011w@iag1|Solution 11 | test111@iag1|T 11 | 01-16-2012 | 01-23-2012 | Taylor's formula and Taylor series |

Sheet 12 | loesungen12.pdf@hm1mach2011w@iag1|Solution 12 | test112@iag1|T 12 | 01-23-2012 | 01-30-2012 | Integration, Integration by parts, substitution formula |

Sheet 13 | loesungen13.pdf@hm1mach2011w@iag1|Solution 13 | test201@iag1|T 13 | 01-30-2012 | 02-06-2012 | Elementary differential equations, initial value problems |

Sheet 14 | loesungen14.pdf@hm1mach2011w@iag1|Solution 14 | | 02-06-2012 | | Repetition |

## Mandelbrot contest

For more details follow this line Mandelbrot contest.

More pictures you can find here: Fractals.

# 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

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

The examinations in Advanced Mathematics will take place on February 18, 2012. 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,
- any one mathematical text book.

It is not allowed to use any electronical devices (calculator, etc.) and collections of old exams or other material.

# Collections of old exams

You can buy copies from old exams (including solutions) at the students's council/union of the department of Mechanical Engineering (Fachschaft Maschinenbau/Chemieingenieurwesen). Link to their Homepage . Note that the old exams are only available in German language at the moment.

Note also that we don't take responsibility for the correctness of the copies.

# 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.