Numerik II

News and Important Remarks

• You can have a look on your Klausur on Wednesday, April, 22, between 11.00 and 13.00 o'clock in Arnimallee 6, room 122.

• The results of the Nachlausur can be found here.

• You can have a look on your Klausur on Thursday, February, 19, between 11.00 and 13.00 o'clock in Arnimallee 6, room 131 (Secretary Nordt).

• The results of the Klausur can be found here.

• The Klausur takes place in the ZIB lecture room.

• Attention: for problem 4 on exercise 4, the method of Runge is not suitable, please use Runge-Kutta-4 instead. The corrected version of the exercise sheet can be found here. The presentation of problem 4 will be postponed to November, 25.

• Attention: there is a mistake on exercise 1, in problem 3 entry \(a_{22} = -1\) not \(-1/25\), you can find the corrected version of the exercise sheet here.

• There are now some Matlab programs to play around available on this homepage (see below).

Dates

General Information

Description

Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

Target Audience

Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites:

Basics of calculus (Analysis I,II) linear algebra (Lineare Algebra I,II) and numerical analysis (Numerik I)

Registration

All participants should register at the KVV, so that we know who is participating. The overall number of participants is also necessary to justify the equipment of the course. In addition, depending on your program of study, you have to register in the Campus Management.

Exercises and Criteria for a Certificate

Tutorial & Exercises

• The tutorial offers the possibility to discuss and better understand the presented material and exercises. Furthermore solutions of exercises are presented by the students.
• A sheet with exercises will be handed out each Tuesday during the lecture. These exercises are also available electronically on this web page (see below).
• The exercises are intended to be solved by teams of three members.
• The exercises consist of theoretical and numerical problems. The latter should be solved using Matlab (available at the students computer pool at the institute). Both types of exercises are rated seperately.
• The solutions have to be finished before the tutorial two weeks after they were handed out.
• The solutions of the numerical problems should be delivered by email to mawolf{at}math.fu-berlin.de. Note that a complete solution for a numerical experiment consists of a running Matlab code, a program executing the required test runs, and protocols of the execution of these test runs. Delivering a correct and running code without knowing what is going on in the code will be regarded and rated as attempt of deception.
• The solutions of the theoretical problems have to be presented in the tutorial on request (without regard to preference and presence) by a member of a given group.

Klausur

• There will be a Klausur on 03.02.2015.
• Students who fail in the Klausur have a second chance in the Nachklausur, which will take place on 10.04.2015.

Criteria for the Certificate

Neccessary and sufficient for a certificate are:

• written exam: passing the Klausur or the Nachklausur (the better grade counts)
• active participation: at least as much success as failure in the presentation of the solution of theoretical problems and 50% of the maximal number of points for numerical problems
• constant participation: 85% attendence in the tutorial (not checked)

Certificates are graded according to the result of the Klausur.

Exercises

• exercise 1
• exercise 2
• exercise 3
• exercise 4
• exercise 5
• exercise 6
• exercise 7
• exercise 8
• exercise 9
• exercise 10
• exercise 11

Matlab programs

Here you can find some Matlab programs to play around.

Accompanying Material

Lecture Notes:

The lecture notes are available here.

The lecture notes Numerics I, in german only.

Matlab:

Here you can find an introduction to Matlab (in german, sorry).

Literature

The following selection of textbooks can be found in the reserved books section (Handapparat) on numerical mathematics in the institutes library (Arnimallee 3) opposite to the reception.

1. Deuflhard, Peter: Newton Methods for Nonlinear Problems. Springer, Berlin, 2004.
2. Deuflhard, Peter und Folkmar Bornemann: Numerische Mathematik II - Gewöhnliche Differentialgleichungen. Walter de Gruyter, Berlin, 2002.
3. Deuflhard, Peter und Folkmar Bornemann: Scientific computing with ordinary differential equations. Springer, Berlin, 2002.
4. Deuflhard, Peter und Andreas Hohmann: Numerische Mathematik I - Eine algorithmisch orientierte Einführung. Walter de Gruyter, Berlin, 2002.
5. Golub, Gene und Charles Van Loan: Matrix computations. Johns-Hopkins-University Press, Baltimore, 1993.
6. Hairer, Ernst, Syvert Paul Nørsett und Gerhard Wanner: Solving Ordinary Differential Equations I - Nonstiff Problems, Band 8 der Reihe Springer Series in Computational Mathematics. Springer, Berlin, Heidelberg, New York, 1987.
7. Hairer, Ernst und Gerhard Wanner: Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems, Band 14 der Reihe Springer Series in Computational Mathematics. Springer, Berlin, Heidelberg, New York, 1991.
8. Meister, Andreas: Numerik linearer Gleichungssysteme. Vieweg, Braunschweig, 1999.
9. Ortega, James und Werner Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1972.
10. Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 1. Springer, Berlin, 2002.
11. Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 2. Springer, Berlin, 2002.
12. Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005. aus dem FU-Netz auch Online verfügbar: http://www.springerlink.com/content/q1x448/fulltext.pdf.
13. Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 2. Springer, Berlin, 2005. aus dem FU-Netz auch Online verfügbar: http://www.springerlink.com/content/v76507/fulltext.pdf.
14. Walter, Wolfgang: Gewöhnliche Differentialgleichungen - eine Einführung. Springer, Berlin, 1996.
15. Werner, Dirk: Funktionalanalysis. Springer, Berlin, 2000.

Further literature on numerics is deposited under the shelf marks H.1.0 and H.1.1.

Introductory literature in computer science can be found under XA.1, introductions in Unix operating system under XD.4.0.

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