Numerical Programming I - Winter 08
- Term
- Winter 08
- Lecturer
- Univ.-Prof. Dr. Hans-Joachim Bungartz
- Time and Place
- t.b.a., room 02.07.023, first lecture: t.b.a.
- Audience
- Computational Science and Engineering, 1st semester
- Tutorials
- t.b.a.
- Exam
- t.b.a.
- Semesterwochenstunden / ECTS Credits
- 6 SWS / 8 Credits
- TUMonline
- {{{tumonline}}}
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
(Material will be updated throughout the semester)
- 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: The Symmetric Eigenvalue Problem
- Chapter 7: Iterative Methods: Roots and Optima
- Chapter 8: Ordinary Differential Equations
Tutorial
Tutorial:
- Exercise 1: Mathematical Essentials
- Exercise 2: Linear Algebra
- Exercise 3: Calculus of one Variable
- Exercise 4: Calculus of Several Variables
- Exercise 5: Stochastics and Statistics (Normal Distribution Table)
- Exercise 6: Floating Point Numbers and Condition
- Exercise 7: Interpolation I
- Exercise 8: Interpolation II
- Exercise 9: Numerical Quadrature
- Exercise 10: Direct Methods for Solving Linear Systems for Equations
- Exercise 11: Symmetric Eigenvalue Problem
- Exercise 12: Iterative Methods: Roots and Optima
Exam
A written exam will be offered at the end of the lecture period.
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
- Press, Flannery, Teukolsky, Vetterling: Numerical Recipes
Cambridge University Press, [1]
- Golub, Ortega: Scientific Computing: An Introduction with Parallel
Computing Academic Press, 1993