Numerical Programming I - Winter 09

Term

Winter 09

Lecturer

Univ.-Prof. Dr. Hans-Joachim Bungartz

Time and Place

Lecture: Tuesday 9:00 - 10:30, lecture room 02.07.023; Thursday 12:00 - 13:30, lecture room 02.07.023

Tutorial: Monday, 14:15 - 15:45, lecture room 02.07.023

Audience

Computational Science and Engineering, 1st semester (module IN2156)

Tutorials

Stefanie Schraufstetter

Exam

February 5th at 14:15 in the lecture room MW 2050 (mechanical engineering building).

Semesterwochenstunden / ECTS Credits

6 SWS (4V + 2Ü) / 8 Credits

TUMonline

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News

Date and time of repeat exam and exam review are fixed now (see exam info).

Contents

This course provides an overview of numerical algorithms. Topics are:

• Floating point arithmetics
• Solving Linear systems
• Interpolation
• Quadrature
• Eigenvalue problems
• Basics of iterative methods
• Basics of numerical methods for ordinary differential equations

The course will start with a short revision of mathematical foundations for numerical algorithms.

Lecture Notes

• Introduction and Literature
• Chapter 1: Foundations of Numerics from Advanced Mathematics
• Chapter 2: Motivation and Introduction
• Chapter 3: Interpolation
• Chapter 4: Numerical Quadrature
• Chapter 5: Direct Methods for Solving Linear Systems of Equations
• Chapter 6: Iterative Methods: Roots and Optima (12.01.: updated!)
• Chapter 7: The Symmetric Eigenvalue Problem
• Chapter 8: Ordinary Differential Equations
• Chapter 9: Hardware-Aware Numerics

Tutorial

Here are the sheets for the tutorial:

• Exercise 1: Mathematical Essentials (solution)
• Exercise 2: Linear Algebra (solution)
• Exercise 3: Calculus of one Variable (solution)
• Exercise 4: Calculus of Several Variables (solution)
• Exercise 5: Stochastics and Statistics (Normal Distribution Table, solution)
• Exercise 6: Floating Point Numbers and Condition (solution, Matlab code)
• Exercise 7: Interpolation I (solution, Matlab code)
• Exercise 8: Interpolation II (solution, Matlab code) (the noise in the programming exercise has to be in[-1,1] instead of [0,1])
• Exercise 9: Numerical Quadrature (solution, Matlab code)
• Exercise 10: Direct Methods for Solving Linear Systems of Equations (solution, Matlab code (zip), (rar))
• Exercise 11: It. Methods for Roots, Eigenvalues I (solution, Matlab code)
• Exercise 12: Eigenvalues II and ODEs (solution, Matlab code)
• Repetition (exercises taken from previous exams, there will be no solution)

Further links:

• Normal Distribution Table
• Java applets for Fourier transform: applet 1 and applet 2 (of course, there exist much more...)
• More about gradient methods of Chap. 6: Painless CG

Organization:

The sheets will be available one week before being discussed in the tutorial. Some of the exercises are marked with a black triangle. It is recommended to prepare and to solve at least these problems either on your own or within a small group in the week before because these problems will be discussed in the tutorial only very shortly. After the tutorial, a solution of all problems will be available.

In the first weeks, the "Foundations of Numerics from Advanced Mathematics" will be repeated. If you are already familiar with all the contents of this chapter and if you can solve the exercise sheets 1-5 quickly on your own, it is not necessary to attend the course during the first weeks. But, since usually everybody learns some new (or forgotten ;-)) facts, we advise to join at least the lecture.

Beginning with sheet 6, there will also be programming assignments, that are marked with a 'P', on the sheet. Solve these problems with MATLAB on your own or in a small group. A solution will be demonstrated and discussed in the tutorial and available on the webpage. It is highly recommended to do these programming assignments, since they are also relevant for the exam!

Exam

The results of the exam are available now via TUMonline. The exam review will be on Monday, April 19th, 2010, 10:00-10:30 in the room 02.05.060. There will not be a possibility for individual appointments for review except for students that have to do the repeat exam.

The repeat exam will also take place on April 19th, 2010 (in the afternoon). For the repeat exam, you have to register again via TUMonline and contact me (schraufs@in.tum.de) for more details.

Literature

• Stoer, Bulirsch: Numerische Mathematik, Springer-Verlag, part 1 (8. edition 1999) and part 2 (4. edition 2000)
• Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 3. edition 2002
• Dahlquist, Björck: Numerical Methods in Scientific Computing: Volume 1 & 2, SIAM 2008, extracts of part 1, part 2
• Press, Flannery, Teukolsky, Vetterling: Numerical Recipes, Cambridge University Press
• Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993

How to get ebooks?

1. Go to the Online Catalogue of the TUMm library and log in with your account

2. Insert keywords for a search request and choose "Electronic Resources = Online Resource" and "type of Publication = Book"

You will find there for example "Schaback, Wendland: Numerische Mathematik"

A special website of the library with links can be found here, e.g. for

• Online Mathematics Textbooks
• Safari books

Note that the proxy server has to be configured correctly! You have to use the proxy http://pac.lrz-muenchen.de