# Numerics II

## News

The video exams will not be carried out with Skype, but by using 'webex' - the official video conference tool of Freie Universität. You will get an individual invitation to your video exam. To enter your video exam, please click on the link provided and follow the instructions from there (which depend on your actual operating system). Enter the video exam at the time it is scheduled.

The oral exam will be carried out together by Ralf Kornhuber and Xingjian Zhang-Schneider. The video conference tool will be announced in time (it will be more professional than Skype). The oral exam will address basic aspects of the four topics presented in the course Numerics II corresponding to the four chapters of the manuscript. The examiners will ask questions and the student will answer. The questions will typically range from easy to difficult, but exceptions are possible. The students will have the choice of the topic to begin with. Please keep pencil and paper ready.

In order to prepare for the exam, We recommend to go through the course and make clear which problem is treated and how it is treated, ranging from in principle to in detail. Here, one could think of possible questions and answers. Practise speaking, organize a Skype meeting with a fellow student and start mutual examinations.

The announced second exam on April, Friday 3 at 10 a.m. is cancelled, because, due to corona pandemie, in-person assessments at FU Berlin will not take place but need to be done in a different format or at a later point in time. We therefore decided to transform the fomat of the second exam from a written examination to an oral examination via skype. The oral examinations will take place during April 6 and 7, 2020. If you want to participate, then please contact Katja Engel (Ekaterina.Engel@fu-berlin.de) until March 27, 2020, at the latest.

The results of the first exam can be found here.

## Dates

Lecture | Mon, 14 - 16 | Arnimallee 6, SR 007/008 | Prof. Dr. Ralf Kornhuber |

Tue, 14 - 16 | Arnimallee 6, SR 007/008 | ||

Tutorial | Thu, 16 - 18 | KöLu24-26/SR 006 Neuro/Mathe | Xingjian Zhang-Schneider |

Exam | Mon, 10.02.2020, 14-16 | Takustr. 9, Gr. Hörsaal | |

Second exam (oral) | April 6 and 7, 2020 | please contact Katja Engel (Ekaterina.Engel@fu-berlin.de) |

## General Information

### Description

Extending basic knowledge on odes from Numerics 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. 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.
- Each week a sheet with exercises will be made 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 a week after they were handed out.
- The solutions of the numerical problems should be delivered by email to xingjian@zedat.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.

### Criteria for the Certificate

- Written exam
- Accomplishment of 60% of the theory points
**and**programming points, respectively. - Regular participation in the tutotials (85% attendance at the tutorials and presentation of an exercise).
- The grade of this course based only on the result of the written exam.

### Exercises

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Exercise 12
- Exercise 13
- Exercise 14

## Accompanying Material

### Lecture Notes

Example programs for exercises can be found here.

The lecture notes are available here. Lecture notes for Numeric I are also available here (only in German).

### Matlab

- Here you can find an introduction to Matlab (in german, sorry).
- Example programs in Matlab can be found here.

## Literature

The following selection of textbooks can be found in the library.

- Deuflhard, Peter: Newton Methods for Nonlinear Problems. Springer, Berlin, 2004.
- Deuflhard, Peter und Folkmar Bornemann: Numerische Mathematik II - Gewöhnliche Differentialgleichungen. Walter de Gruyter, Berlin, 2002.
- Deuflhard, Peter und Folkmar Bornemann: Scientific computing with ordinary differential equations. Springer, Berlin, 2002.
- Deuflhard, Peter und Andreas Hohmann: Numerische Mathematik I - Eine algorithmisch orientierte Einführung. Walter de Gruyter, Berlin, 2002.
- Golub, Gene und Charles Van Loan: Matrix computations. Johns-Hopkins-University Press, Baltimore, 1993.
- 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.
- 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.
- Meister, Andreas: Numerik linearer Gleichungssysteme. Vieweg, Braunschweig, 1999.
- Ortega, James und Werner Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1972.
- Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 1. Springer, Berlin, 2002.
- Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 2. Springer, Berlin, 2002.
- 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.
- 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.
- Walter, Wolfgang: Gewöhnliche Differentialgleichungen - eine Einführung. Springer, Berlin, 1996.
- 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

Prof. Dr. Ralf Kornhuber | ralf.kornhuber@fu-berlin.de | Arnimallee 6, Room 130 open consultation hours: Tue 11-12 |

Xingjian Zhang-Schneider (Assistent) | xingjian@zedat.fu-berlin.de | Arnimallee 9, Raum 125 consultation hours: on appointment |