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(winter 2005/2006) 
Audience:
 students in Computational Science
and Engineering (CSE, compulsory course)
 students in Informatik (Hauptstudium, vertiefende Vorlesung in Theoretische Informatik)
 students in Physik (Hauptstudium, nichtphysikalisches Wahlfach)
 students in Mathematik and Technomathematik and other scientific subjects (Wahlfach)
 students of the vhb (Virtuelle Hochschule Bayern)
Time and Place:
Tuesday 12:3014:00,
lecture room MI 02.07.023,
first lesson Oct 25
Final Exam:
The results of the exam are published at the CSE black board
(2nd floor, between wings 5 and 7). Please contact the lecturer
about exam review (Klausureinsicht) or repeat exams (for those who
did not pass; repeat exams will be oral exams).
 For students in Computational Science and Engineering
the exam is only the first part of the exam in the module
"Introduction to Scientific Computing"  the second part of the
exam will be taken in summer term 2006 ("Scientific Computing II").
 Students in all other subjects will receive a graded certificate
("benoteter Semestralschein"), if they pass the exam.
If you want to take the exam as "studienbegleitende Prüfung",
please contact the lecturer and the examination board in charge.
Possible Exam Questions
Generated by the students during the lectures:
The questions are a good collection for preparing for the exam.
However, exam questions are not restricted to this collection, of course.
Contents:
This course provides an overview of scientific computing, i. e. of the
different tasks to be tackled on the way towards powerful
numerical simulations. The entire "pipeline" of simulation is discussed:
 mathematical models:
derivation, analysis, and classification
 numerical treatment of these models:
discretization of (partial) differential systems, grid generation
 efficient implementation of numerical algorithms:
implementation on monoprocessors vs. parallel computers
(architectural features, parallel programming, load distribution,
parallel numerical algorithms)
 interpretation of numerical results & visualization

 validation
The course is conceived as an introduction to the thriving field of
numerical simulation for computer scientists, mathematicians, engineers,
or natural scientists without an already strong background in
numerical methods.
Lecture Notes:
 Oct 25:
Introduction: Scientific Computing as a Discipline
(slides,
handout)
 Nov 8:
Fibonacci's Rabbits, Classification of Models
(slides,
handout)
 Nov 15:
Continous Population Models
(slides,
handout;
Maple worksheets:
popmodel.mws,
lotkavolt.mws)
 Nov 22:
Continous Population Models (cont)
(slides,
handout;
Maple worksheets:
dirfields.mws)
 Nov 29:
Numerical Methods for ODE
(slides,
handout;
Maple worksheets:
numerics_ode.mws)
 Dec 6:
Numerical Methods for ODE
(slides,
handout;
Maple worksheet:
numerics_ode.mws)
Discrete Models for the Heat Equation
(slides,
handout;
Maple worksheet:
poisson2D.mws)
 Dec 13:
Heat Equation  Analytical and Numerical Solution
(slides,
handout;
Maple worksheets:
heat1D_disc.mws,
heat1D_impl.mws)
Additional material:
(discrete energy: handout;
Maple worksheet on Fourier's method: heat1D_four.mws)
 Dec 20:
Grid Generation
(slides,
handout)
 Jan 10:
Discretisation of PDE
(slides,
handout;
Maple vorksheet:
poisson2D.mws,
fe.mws)
 Jan 17:
Discretisation of PDE
(slides,
handout;
Maple vorksheet:
fe.mws)
 Jan 24:
Conclusion and Outlook
(slides,
handout)
Literature
 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
Michael Bader