### Advanced Mathematics II (Summer Semester 2011)

- Lecturer: PD Dr. Frank Hettlich
- Classes: Lecture (3102001), Problem class (3102002)
- Weekly hours: 4+2

**This is the homepage for class in Advanced Mathematics II in the summer semester 2011.**

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

Lecture: | Tuesday 14:00-15:30 | ID SR Raum 203 |

Wednesday 8:00-9:30 | ID SR Raum 203 | |

Problem class: | Thursday 9:45-11:15 | ID SR Raum 202 |

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

Lecturer | PD Dr. Frank Hettlich | |

Office hours: Wednesday 10:30am - 12am and on appointment | ||

Room 1.042 Kollegiengebäude Mathematik (20.30) | ||

Email: frank.hettlich@kit.edu | ||

Problem classes | Dr. Janina Stompe | |

Office hours: | ||

Room 1.048 Kollegiengebäude Mathematik (20.30) | ||

Email: janina.stompe@kit.edu |

# Content

The Topics of the lecture are:

- vector spaces
- differential equations
- the Laplacetransformation
- vector valued functions in several variables

# Tutorial

The tutorials take place on tuesday, 17:30-19:00.

# Problem Sheets

In the summer semester 11 problem sheets will be handed out, containing problems that are relevant for the exam. The problem sheets will be handed out in class. However, but you can also download them here in the PDF format.

Sheet | Solutions | Date | Due | Topics |

1st Sheet | solution1 | 12.04.2011 | 21.04.2011 | elementary differential equations |

2nd Sheet | solution2 | 21.04.2011 | 29.04.2011 | linearly dependent, basis, dimension |

3rd Sheet | solution3 | 28.04.2011 | 06.05.2011 | Euclidian vector spaces, linear maps |

4th Sheet | solution4 | 05.05.2011 | 13.05.2011 | Linear map, matrix calculus |

5th Sheet | solution5 | 12.05.2011 | 20.05.2011 | determinants, change of bases |

6th Sheet | solution6 | 19.05.2011 | 27.05.2011 | eigenvalues, eigenvectors |

7th Sheet | solution7 | 26.05.2011 | 03.06.2011 | Euler differential equation, reduction of the order |

8th Sheet | solution8 | 31.05.2011 | 10.06.2011 | linear systems, Wronskian, method of undetermined coefficients |

9th Sheet | solution9 | 09.06.2011 | 17.06.2011 | variation of the constants, power series method |

10th Sheet | solution10 | 16.06.2011 | 24.06.2011 | parameter integrals, Laplace transform, numerics for ODEs |

11th Sheet | solution11 | 21.06.2011 | 01.07.2011 | Laplace transform, initial value problems, convolution theorem |

12th Sheet | solution12 | 30.06.2011 | 08.07.2011 | convolution, vector valued functions |

13th Sheet | solution13 | 07.07.2011 | --- | some examples |

# The testat

If you attend succefully the problem session, you will get a testat (Pruefungsvorleistung). There will be 11 problem sheets containing problems that are relevant for the exam. These will be corrected by your tutor. Only the sheets 1 to 10 will count for the testat which is a requirement for participating in the exam. To gain the testat, at total of 125 points has to be achieved from sheets 1 to 10. Furthermore, on 8 of these sheets, a minimum of 5 point is required.

# Additional material

- Maple Worksheets for the AM lectures

# Examination

At the end of every semester, an examination in *Advanced Mathematics II* will take place (normally in July/August and in February/March). Having successfully obtained the testat is a requirement for participation.

The following materials may be used during the examination:

- The lecture notes for AM I and II including your handwritten notes,
- a handbook of formulae,
- an additional mathematical work.

Electronic devices (such as a pocket calculator) and collections of exam papers or loose sheets of paper are not allowed.

# 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). - K. Burg, H. Haf, F. Wille:
*Höhere Mathematik für Ingenieure.*Volumes I-III. Teubner Verlag, Stuttgart (in German). - J. Stewart:
*Calculus, Early Transcendentals.*Brooks/Cole Publishing Company. - G. James:
*Advanced Modern Engineering Mathematics.*(4th edition) Pearson, 2011.