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Advanced Mathematics II (ID) (Summer Semester 2012)

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

This is the homepage for the Advanced Mathematics II class in the summer semester 2012.


+++ Examination in AM1, AM2 and AM3 +++

You can find detailed information to the exams on the following sites:
Exam in Advanced Mathematics 1
Exam in Advanced Mathematics 2
Exam in Advanced Mathematics 3


Schedule
Lecture: Monday 9:45-11:15 ID SR Raum 202
Wednesday 8:00-9:30 ID SR Raum 203
Problem class: Thursday 11:30-13:00 ID SR Raum 202
Lecturers
Lecturer Prof. Dr. Maria Axenovich
Office hours: Mon. 13:00-14:00
Room 1.043 Kollegiengebäude Mathematik (20.30)
Email: maria.aksenovich@kit.edu
Problem classes Dipl.-Math. Marc Mitschele
Office hours:
Room 3A-11.2 Allianz-Gebäude (05.20)
Email: marc.mitschele@kit.edu

Content

The topics of the lecture are:

  • vector spaces
  • differential equations
  • the Laplace transformation
  • vector valued functions of several variables

Tutorial

We offer a tutorial, where a tutor (Weixuan Zhang, zhangweixuanpeter@googlemail.com , a senior student) discusses problems/problem sheets with you. This tutor will also correct your homework.
During the semester the tutorial will take place each Friday from 2 to 3:30 pm, in the seminar room ID SE 203.
Please note that the tutorials start on April 20th, 2012.


Problem Sheets

Every week, a new worksheet with 5 problems will be handed out. On each problem you can get up to 10 points. Your solutions must be handed in the next week. Please hand in your homework into the AM2-box near seminar room Z1, building 01.85 (Fritz-Erler-Str. 1-3) or give it to your tutor.

During the semester you will find more information on problems here. Additionally we offer some practice tests.

The problem sheets will be handed out in class. You can also download them as pdf-files below.

Sheet Solutions Test DateDueTopics
Sheet 1loesungen1.pdf@hm2mach2012s@iag1|Solution 1test202@iag1|T 2 18.04.12 25.04.12 Vector spaces, linear combinations, intersections
Sheet 2loesungen2.pdf@hm2mach2012s@iag1|Solution 2test202@iag1|T 2 25.04.12 02.05.12 Linear dep./indep., span, dimension, lines and planes
Sheet 3loesungen3.pdf@hm2mach2012s@iag1|Solution 3test203@iag1|T 3 02.05.12 09.05.12 Matrices, linear mappings, rotation, reflection
Sheet 4loesungen4.pdf@hm2mach2012s@iag1|Solution 4test203@iag1|T 3 , test204@iag1|T 4 09.05.12 16.05.12 Linear systems, regular and singular matrices, determinant
Sheet 5loesungen5.pdf@hm2mach2012s@iag1|Solution 5test204@iag1|T 4 , test205@iag1|T 5 16.05.12 23.05.12 Determinants, eigenvalues, eigenvectors
Sheet 6loesungen6.pdf@hm2mach2012s@iag1|Solution 6test206@iag1|T 6 23.05.12 30.05.12 Differential equations, constant coefficients, Euler type, reduction of the order
Sheet 7loesungen7.pdf@hm2mach2012s@iag1|Solution 7test207@iag1|T 7 30.05.12 06.06.12 Systems of differential equations, fundamental system, Wronskian, initial value problems
Sheet 8loesungen8.pdf@hm2mach2012s@iag1|Solution 8test208@iag1|T 8 06.06.12 13.06.12 Initial value problems, undetermined coefficients
Sheet 9loesungen9.pdf@hm2mach2012s@iag1|Solution 9test208@iag1|T 8,test209@iag1|T 9 13.06.12 20.06.12 Variation of parameters, reduction of the order, power series ansatz
Sheet 10loesungen10.pdf@hm2mach2012s@iag1|Solution 10test209@iag1|T 9 20.06.12 27.06.12 Generalized power series, Euler's method, parameter integrals
Sheet 11loesungen11.pdf@hm2mach2012s@iag1|Solution 11test210@iag1|T 10,test211@iag1|T 11 27.06.12 04.07.12 Partial fraction decomposition, Laplace transform, Heaviside function, initial value problems
Sheet 12loesungen12.pdf@hm2mach2012s@iag1|Solution 12test211@iag1|T 11 04.07.12 11.07.12 Laplace transform and initial value problems, convolution, distributions
Sheet 13loesungen13.pdf@hm2mach2012s@iag1|Solution 13test212@iag1|T 12 11.07.12 18.07.12 Vector valued functions of several variables, norms, differentiability, linearisation, chain rule

The testat

If you successfully work on the home work and the in class quizzes, 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 II 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:

  • obtain at least 135 points on worksheets 1 to 11. This is approximately 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.
  • Each week there will be a short in class quiz, which is worth 5 points maximum. You need to get at least 30 points on 12 quizzes and obtain at least 1 point on each of at least 10 quizzes.

Additional material

Examination

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

The examinations in Advanced Mathematics II will take place on August 4, 2012, 9.00-11.00 am. During the exam the use of the following materials is allowed:

  • the AM I and AM II lecture notes including any handwritten notes in your copy,
  • a printed book of formulae,
  • one mathematical text book.

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

References

Besides the lecture notes, we 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).
  • C.H. Edwards, D.E. Penney: Elementary Differential Equations with Boundary Value Problems. Prentice Hall, 6th ed.
  • P.R. Halmos: Finite-Dimensional Vector Spaces. Princeton, N.J., 2nd ed.
  • J. Hefferon: Linear Algebra. Free textbook, can be downloaded from the author's webpage: here.
  • G. James: Advanced Modern Engineering Mathematics. (4th edition) Pearson, 2011.
  • D.C. Lay: Linear Algebra and Its Applications. Addison Wesley, 4th ed.
  • J. Stewart: Calculus, Early Transcendentals. Brooks/Cole Publishing Company.