Numerical Programming I - Winter 08: Difference between revisions

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= Lecture Notes =
= Lecture Notes =


(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)
(Material will be updated throughout the semester)


* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_intro.pdf Introduction and Literature]
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_intro.pdf Introduction and Literature]
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_01.pdf Chapter 1:] Foundations of Numerics from Advanced Mathematics
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_01.pdf Chapter 1:] Foundations of Numerics from Advanced Mathematics
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_02.pdf Chapter 2:] Motivation and Introduction
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_02.pdf Chapter 2:]  
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_03.pdf Chapter 3:] Interpolation
Motivation and Introduction
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_04.pdf Chapter 4:] Numerical Quadrature
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_05.pdf Chapter 5:] Direct Methods for Solving Linear Systems of Equations
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_03.pdf Chapter 3:]  
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_06.pdf Chapter 6:] The Symmetric Eigenvalue Problem
Interpolation
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_07.pdf Chapter 7:] Iterative Methods: Roots and Optima
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_08.pdf Chapter 8:] Ordinary Differential Equations  
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_04.pdf Chapter 4:]  
Numerical Quadrature
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_05.pdf Chapter 5:]  
Direct Methods for Solving Linear Systems of Equations
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_06.pdf Chapter 6:]  
The Symmetric Eigenvalue Problem
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_07.pdf Chapter 7:]  
Iterative Methods: Roots and Optima
 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_08.pdf Chapter 8:]  
Ordinary Differential Equations  




Revision as of 11:01, 21 July 2008

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 - 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
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