Numerik II

News and Important Remarks

• You can have a look on your Klausur on Wednesday, 4.4. and Thursday, 5.4. between 15:00 and 16:30 o'clock in Arnimallee 6, room 131 (Secretary Nordt).

• Here you can find the results of the Nachklausur.

• The Nachklausur on thursday, 15.3.2012 takes place in the ZIB lecture room, it starts at 10:15 o'clock and lasts 90 minutes. Please arrive at least 10 minutes in advance. Pleace bring a valid identity card or passport with you and put it out on your desk in the beginning. You are allowed to use all your written documents, books, and a non-programmable calculator. Please do not use a pencil.

• There will be a discussion of the Klausur-problems both in the lecture on wednesday, 15.2. and in the tutorial on thursday 16.2.

• You can have a look on your Klausur on thursday, 16.2. and friday, 17.2. between 15.00 and 17.00 o'clock in Arnimallee 6, room 131 (Secretary Nordt).

• Here you can find the results of the Klausur.

• The Klausur on wednesday, 8.2.2012 takes place in Arnimallee 3 HS 001, it starts at 10:15 o'clock and lasts 90 minutes. Please arrive at least 10 minutes in advance. Pleace bring a valid identity card or passport with you and put it out on your desk in the beginning. You are allowed to use all your written documents, books, and a non-programmable calculator. Please do not use a pencil.

• On exercise sheet 9 there will be 3 extra programming points for solving the Keppler-Problem for an earth-moon system numerically with the method you should implement in problem 3.

• In problem 2 on exercise sheet 4 \(|x_0| < \delta \) should be chosen sufficiently small!
• There are two mistakes on the second exercise sheet: In problem 1 a) the first equation should be \(x_1' = -x_1 + x_2^2\), and in problem 2 the solution is \(x(t) = x_0 / (1 - \lambda|x_0|t) \). You can find the corrected version here.
• The MATLAB-function you should use for visualization in problem 2 on the first exercise sheet is called odephas2, not odephase2.

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 fundamental properties of various multistep approaches. In the second part of this lecture we consider the numerical solution of eigenvalue problems and large linear systems. As a first glance in the direction of pdes, we plan to conclude with some remarks on the method of lines for linear and nonlinear parabolic problems.

Target Audience

Students of the Diploma, Bachelor, Master and BMS course of studies

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. In this way, we learn who is participating in the course and get a basis for organising the exercises. The overall number of participants is also necessary to justify the equipment of this course.

In addition, depending on your program of study, you have to register in the following way:

• BMS students have to register via e-mail at the one-stop office.
• Studierende im Campus Management verwalteter Bachelor- und Masterstudiengänge müssen sich eigenverantwortlich und verbindlich über das Campus Management an- bzw. abmelden. Über Möglichkeiten und Pflichten zur An- und Abmeldung gibt die Homepage des Campus Managements Auskunft. Für Fragen ist ferner eine Hotline unter 838-77777 sowie eine E-Mail-Adresse cm-hotline@fu-berlin.de eingerichtet.
• Für Studierende der Bioinformatik alter Studienordnung ist die Anmeldung im KVV verbindlich. Im Fall eines Rücktritts ist die Abmeldung bis 31.10.2011 im KVV erforderlich.
• Die Anmeldung im KVV ist für Diplom- und Staatsexamenskandidaten alter Studienordnung (nicht Bachelor/Master) ausreichend. Im Falle eines Rücktritts ist keine Abmeldung nötig.

Exercises and Criteria for a Certificate

Tutorial & Exercises

• A sheet with exercises will be handed out each Wendsday during the lecture. These exercises are also available electronically on this web page (see below).
• The tutorials offer the possibility to ask questions regarding the presented material. Furthermore future and previous exercises are discussed in the tutorials. The first tutorial takes place on Thursday, October 27, 2011. Active participation in the tutorial is not only fundamental for the understanding of the presented material but also for a successful Klausur.
• The exercises are intended to be solved by teams of two to three members. Please remember to annotate the name of all participating team members on the completed exercises.
• The solutions have to be finished before the tutorial on thursday 12 o'clock in the week after they were handed out. Please put your exercises into the box with the name 'Wolf' on it, found in the first floor in Arnimallee 3. You can also hand them in at the beginning of the tutorial.
• The exercises consist of theoretical problems as well as numerical experiments. Both types of exercises are rated seperately by an appropiate number of either theory points (TP) or programing points (PP). Numerical experiments have to be handled using Matlab (available at the students computer pool at the institute). 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. Please deliver your programs by e-mail as well as printed out to the tutor. Don't forget to mention all team members in your e-mails and programs.
• Caution: Delivering a correct and running code without knowing what's going on in the code will be regarded and rated as attempt of deception.

Klausur

• There will be a Klausur at the end of the semester. Only those students who achieved at least 50% of the maximal theory points and 50% of the maximal programing points are allowed to participate at the Klausur. This rule does not apply to students inscribed in a course of studies organized by the Campus Management who are allowed to participate in any case.
• Students who fail in the Klausur have a second chance in the Nachklausur.

Criteria for the Certificate (Übungsschein)

Neccessary and sufficient for a certificate are:

• passing the Klausur or the Nachklausur
• active participation (50% of the maximal theory points and 50% of the maximal programing points)
• constant participation (85% presence in the tutorial) (suspended since November 1, 2010)

Certificates are graded according to the result of the Klausur.

Exercises

• exercise1
• exercise2
• exercise3
• exercise4
• exercise5
• exercise6
• exercise7
• exercise8
• exercise9
• exercise10
• exercise11
• exercise12

Accompanying Material

Lecture Notes:

The lecture notes are available here (corrected version).

The lecture notes NumericsI, 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 in the reserved books section (Handapparat) on numerical mathematics in the institutes library (Arnimallee 3) opposite to the reception and to the left of the door to the journals section.

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.

Contact