Scientific Computing I - Winter 08

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Winter 08
Dr. Michael Bader
Time and Place
Wednesday, 10:15-11:45., lecture hall MI HS 2
Computational Science and Engineering, 1st semester (Module IN2005)
written exam (Feb 4, 2009, 10:00-12:00, MI HS 2 and MI 01.06.011)
Semesterwochenstunden / ECTS Credits
2 SWS (2V) / 3 Credits


  • From Nov 5: change of time and lecture hall to Wed, 10-12, in MI HS 2


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 Scientific Computing 1 is intended for students in the Master's Program Computational Science and Engineering. Students in all other study programs, please consider our lecture Modellbildung und Simulation (see the lecture from summer term 2008, for example), instead.

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 22
slides, handout
Fibonacci's Rabbits, Classification of Models 
Oct 22
slides, handout
Continous Population Models I & II - Single Species Models, Analysis of ODE Models 
Oct 29, Nov 5
Maple worksheet: popmodel.mws
Continous Population Models III & IV - Systems of ODE, Analysis of ODE Systems
Nov 5, Nov 12
slides, handout population models
Maple worksheets: lotkavolt.mws, dirfields.mws
Numerical Methods for ODE 
Nov 19 & 26, Dec 3
slides, handout
Maple worksheet: numerics_ode.mws
Discrete Models for the Heat Equation 
Dec 3, Dec 10
slides, handout
Maple worksheet: poisson2D.mws
Heat Equation - Analytical and Numerical Solution 
Dec 10,17
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)
Discretisation of PDEs, Finite Element Method 
Jan 7, 14, 21
slides, handout
Maple worksheets: poisson2D.mws, fe.mws
Grid Generation 
Jan 28
slides, handout
Case Study - Computational Fluid Dynamics (not included this year)
slides, handout
Conclusion and Outlook 
Feb 28
slides, handout


  • Date of final exam: Wednesday, February 4, 2009.
  • Time and place: 10:00 - 12:00 in rooms MI HS 2 (names/login A-P) and MI 01.06.011 (Q-Z)
  • Helping material: you are allowed to use one sheet (size A4) of paper with hand-written(!) notes during the exam. Any further helping material (books, calculators, etc.) is forbidden!
  • Exam topics are all topics covered during the lectures; see the catalogue of exam questions and previous years' exams below.
  • Repeat exam: a repeat exam will offered (only for students who failed the regular exam) in April or May 2009. The exam will be written or oral, depending on the number of participants.

Catalogue of Exam Questions

The following catalogue contain questions collected by students of the lectures in winter 05/06 and 06/07. The catalogue is intended for preparation for the exam, only, and serves as some orientation. It's by no means meant to be a complete collection.

Last Years' Exams

Please, be aware that there are always slight changes in topics between the different years' lectures. Hence, the previous exams are not fully representative for this year's exam.


  • 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

Online Material