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

# Advanced Mathematics II (Summer Semester 2014)

Lecturer: | Prof. Maria Axenovich Ph.D. |
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Classes: | Lecture (0120010), Problem class (0) |

Weekly hours: | 4+2 |

#### NEWS

exam results | |

22.10.2014 | Exam Review AM 1-3 |

Lecture: | Tuesday 14:00-15:30 | ID SR Raum 202 |
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Thursday 11:30-13:00 | ID SR Raum 203 | |

Problem class: | Tuesday 17:30-19:00 | ID SR Raum 203 |

Lecturer | Prof. Maria Axenovich Ph.D. |
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Office hours: by appointment | |

Room 1.043 Kollegiengebäude Mathematik (20.30) | |

Email: maria.aksenovich@kit.edu | |

Problem classes | Jonathan Rollin |

Office hours: Friday, 15:30-16:30 | |

Room 1.039 Kollegiengebäude Mathematik (20.30) | |

Email: jonathan.rollin@kit.edu |

# Holidays

During summer semester there are lots of public holidays. These are announced here with additional information.

- Friday, 18th April: no tutorial this week (Good Friday)
- Monday, 21st April: (Easter)
- Thursday, 1st May: (International Workers' Day)
- Thursday, 29th May: (Ascension Day)
- Monday, 9th June: (Pentecost)
- Thursday, 19th June: (Feast of Corpus Christi)

# Problem Sheets

A problem sheet will be published every Thursday on this website. Moreover the printouts will be distributed at the ID.

Problem Sheet No. 1 (vectorspaces, linear independence, basis)

Problem Sheet No. 2 (lines, planes, orthogonal projection, distances, scalar product, norm)

Problem Sheet No. 3 (matrix, matrix product)

Problem Sheet No. 4 (linear transformations, inverse matrix)

Problem Sheet No. 5 (basis transformation, determinant)

Problem Sheet No. 6 (basis transformation, eigenvalues, eigenvectors)

Problem Sheet No. 7 (first order differential equations: separable, linear, Bernoulli)

Problem Sheet No. 8 (second/higher order differential equations: linear, homogeneous, Euler)

Problem Sheet No. 9 (systems of differential equations, fundamental system, Wronskian, uniqueness of solutions, reduction of order)

Problem Sheet No. 10 (non-homogeneous differential equations: undetermined coefficients, power series method)

Problem Sheet No. 11 (partial fraction decomposition, improper integrals, Laplace transform)

Problem Sheet No. 12 **This sheet won't be graded!** (partial fraction decomposition, Laplace transform, Convolution, Power Series)

Written solutions of these exercises are due 12 days later, on Tuesday. Please put them into the box at the students office before 2:00 PM.

Students should solve the problems independently, after that they could discuss the solutions in groups of two and could also submit one solution set per group.

The solutions will be corrected and graded by the tutor (Dhruv Singhal).

# 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.

**In order to obtain the testat you need to register in the student portal (https://campus.studium.kit.edu/). It is called "Vorleistung" there.** Please register **before June 30'th!**

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.

# Tutorial

The tutorial takes place Fridays, at 9:45 am.

# Examination

There will be a written exam on Saturday, 26'th of July, from 9:00 - 11:00 am.

You won't be able to register for the exam, if the testat was not given to you. Note that you have to register for the testat as well (see above).

The seating plan will be published few days before the exam.

## Allowed resources

You may bring and use the following resources during the exam:

- the printed lecture notes (AM 1+2) including your own notes, but no additional pages
- a handbook of formulae
- one additional mathematical work

Regarding the last two points: Works without an ISBN have to be checked and signed by one of the examiners on the day prior to the exam at the latest (use the official office hours).

In particular, it is not allowed to use a calculator.

Paper will be brought by us and will be available in any required quantity.