Numerical Programming I - Winter 08
- Term
- Winter 08
- Lecturer
- Dr. Michael Bader
- Time and Place
- Wednesday, t.b.a., Raum 02.07.023, Beginn: 23.10.2008
- Audience
- Computational Science and Engineering, 1. Semester
- Tutorials
- -
- Exam
- written exam (time and day t.b.a.)
- Semesterwochenstunden / ECTS Credits
- 2 SWS / 3 Credits
- TUMonline
- {{{tumonline}}}
Contents
This course provides an overview of numerical algorithms. Topics are:
* Floating point arithmetics * Linear systems * Eigenvalue problems * Interpolation * Quadrature * 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.
- Foundations of numerical algorithms from calculus and linear algebra
- Floating point arithmetic (rounding error analysis, condition, and stability)
- Solving linear systems (Gaussian elimination, LR-factorization, pivoting, least squares, QR-factorization)
- Interpolation (polynomial ~, Spline ~, trigonometric ~, Fast Fourier Transform)
- Quadrature (Newton-Cotes formulae, extrapolation, Gaussian ~)
- Eigenvalue problems (symmetric, non-symmetric)
- Fundamentals of iterative methods (Jacobi and Gauss-Seidel ~, gradient ~, fixed point iteration, Newton ~)
- Basics of numerical methods for ordinary differential equations (Finite Differences, Euler and Runge-Kutta, consistency and convergence)
Lecture Notes and Material
(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)
- Introduction - Scientific Computing as a Discipline
- Oct
- slides, handout
- Fibonacci's Rabbits, Classification of Models
- Oct
- slides, handout
- Continous Population Models I - Single Species Models
- Nov
- slides
- Maple worksheet: popmodel.mws
- Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
- slides, handout population models
- Maple worksheets: lotkavolt.mws, dirfields.mws
- Numerical Methods for ODE
- Nov
- slides, handout
- Maple worksheet: numerics_ode.mws
- Discrete Models for the Heat Equation
- Dec
- slides, handout
- Maple worksheet: poisson2D.mws
- Heat Equation - Analytical and Numerical Solution
- Dec
- slides, handout
- Maple worksheets: Fourier's method: heat1D_four.mws, Discretisation: heat1D_disc.mws, heat1D_impl.mws
- Additional material: Neumann stability (worksheet with solution), discrete energy (handout)
Exam
A written exam will be offered at the end of the lecture period.
Literature
- A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press
- Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition)
- Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
- Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998
- Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
- Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992