### Advanced Mathematics II (Summer Semester 2011)

• Lecturer:
• 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.

# 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,