Numerical Programming I - Winter 08: Difference between revisions

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; Introduction - Scientific Computing as a Discipline : Oct
= Tutorial =
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline_6up.pdf handout]
 
; Fibonacci's Rabbits, Classification of Models : Oct
Tutorial:
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo_6up.pdf handout]
 
; Continous Population Models I - Single Species Models : Nov
* Exercise 1: Mathematical Essentials
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population.pdf slides]
* Exercise 2: Linear Algebra
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/popmodel.mws popmodel.mws]
* Exercise 3: Calculus of one Variable
; Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
* Exercise 4: Calculus of Several Variables
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population2.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population_6up.pdf handout population models]
* Exercise 5: Stochastics and Statistics (Normal Distribution Table)
: Maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/lotkavolt.mws lotkavolt.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/dirfields.mws dirfields.mws]
* Exercise 6: Floating Point Numbers and Condition
; Numerical Methods for ODE : Nov
* Exercise 7: Interpolation I
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/ode_numerics.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/ode_numerics_6up.pdf handout]
* Exercise 8: Interpolation II
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/numerics_ode.mws numerics_ode.mws]
* Exercise 9: Numerical Quadrature
; Discrete Models for the Heat Equation : Dec
* Exercise 10: Direct Methods for Solving Linear Systems for Equations
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatmodel.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatmodel_6up.pdf handout]
* Exercise 11: Symmetric Eigenvalue Problem
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws]
* Exercise 12: Iterative Methods: Roots and Optima
; Heat Equation - Analytical and Numerical Solution : Dec
 
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heateq.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heateq_6up.pdf handout]
: Maple worksheets: Fourier's method: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_four.mws heat1D_four.mws], Discretisation: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_disc.mws heat1D_disc.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_impl.mws heat1D_impl.mws]
: Additional material: Neumann stability ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/scicomp3.pdf worksheet] with [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/solution3.pdf solution]), discrete energy ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatenergy.pdf handout])


= Exam =
= Exam =


A written exam will be offered at the end of the lecture period.
A written exam will be offered at the end of the lecture period.


= Literature =
= Literature =


* A.B. Shiflet and G.W. Shiflet: [http://www.pupress.princeton.edu/titles/8215.html Introduction to Computational Science], Princeton University Press
* Stoer, Bulirsch: Numerische Mathematik
* Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition)
Springer-Verlag, part 1 (8. edition 1999) and part 2 (4. edition 2000)
* Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
* Stoer, Bulirsch: Introduction to Numerical Analysis
* Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998
Springer, 3. edition 2002
* Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
* Press, Flannery, Teukolsky, Vetterling: Numerical Recipes
* Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992
Cambridge University Press, [http://www.nr.com/]
* Golub, Ortega: Scientific Computing: An Introduction with Parallel
Computing
Academic Press, 1993
 
 


[[Category:Teaching]]
[[Category:Teaching]]

Revision as of 11:05, 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)


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

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