Scientific Computing I  Winter 15
 Term
 Winter 15
 Lecturer
 Dr. rer. nat. Tobias Neckel
 Time and Place
 Wednesday, 10:1511:45; HS 2 (starts Oct 21)
 Audience
 Computational Science and Engineering, 1st semester
 Tutorials
 Denis Jarema, time and place: I group: Wednesday, 14:0015:45, MI 02.13.008, II group: Monday, 14:1516:00, MI 03.13.010 (starts Oct 26)
 Exam
 tba
 Semesterwochenstunden / ECTS Credits
 4 SWS (2V+2Ü) / 5 Credits
 TUMonline
 tba
Contents
Announcements
 Starting from 02.11.2015 the tutorial slot on Monday at 16:0018:00 is moved to Wednesday 14:0016:00, room 02.13.008.
Contents
The lecture will cover the following topics in scientific computing:
 typical tasks in the simulation pipeline in scientific computing;
 classification of mathematical models (discrete/continuous, deterministic/stochastic, etc.);
 modelling with (systems) of ordinary differential equations (example: population models);
 modelling with partial differential equations (example: heat equations);
 numerical treatment of models (discretisation of ordinary and partial differential equations: introduction to Finite Volume and Finite Element Methods, grid generation, assembly of the respective large systems of linear equations);
 analysis of the resulting numerical schemes (w.r.t. convergence, consistency, stability, efficiency);
An outlook will be given on the following topics:
 efficient implementation of numerical algorithms, both on monoprocessors and parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
 interpretation of numerical results (visualization)
Lecture Notes and Material
Slides of the lectures, as well as worksheets and solutions for the tutorials, will be published here as they become available.
Day  Topic  Material 

Oct 21  Introduction  CSE/Scientific Computing as a discipline  slides: discipline.pdf, fibo.pdf printing versions: discipline2x4.pdf, fibo2x4.pdf 
Oct 26  Worksheet 1  Worksheet 1, Solution 1 
Nov 2/4  Worksheet 2  Worksheet 2, Solution 2 
Nov 4  Population Models  Continuous Modelling (Parts I to II)  slides: population.pdf python worksheets: Lotka Volterra, Population Models maple worksheets: lotkavolt.mws, popmodel.mw maple_lotkavolt.pdf, maple_popmodel.pdf printing version: population2x4.pdf 
Nov 9/11  Worksheet 3  Worksheet 3, Solution 3 
Nov 11  Population Models  Continuous Modelling (parts III to IV)  slides: population2.pdf printing version: population22x4.pdf 
Nov 16/18  Worksheet 4  Worksheet 4, Solution 4, ws4_ex1.py ipython notebook version: W4Direction_Fields_for_ODE.ipynb 
Nov 18  Numerical Methods for ODEs (part I) 
slides: ode_numerics.pdf python worksheets: Numerics ODE maple worksheets: numerics_ode.mws, maple_numerics_ode.pdf printing version: ode_numerics2x4.pdf 
Nov 23/25  Worksheet 5  Worksheet 5, Solution 5, ws5_ex1.py 
Nov 25  Numerical Methods for ODEs (part II) 
slides: ode_numerics.pdf python scripts for visualisation of stability: unstable explLLM2 example, visualisation of stability regions, explicit midpoint rule examples (Martini glass effec), Martini glass effect in scaled plot 
Nov 30, Dec 2  Worksheet 6  Worksheet 6, Solution 6, ws6_ex3.py 
Dec 2  Heat Transfer  Discrete and Continuous Models  slides: heatmodel.pdf python worksheets: Heat Transfer maple worksheets: poisson2D.mws, poisson2D.pdf printing version: heatmodel2x4.pdf 
Dec 7/9  Worksheet 7  Worksheet 7, Solution 7, ws7_ex1.py 
Dec 9  1D Heat Equation  Analytical and Numerical Solutions  slides: heateq.pdf, heatenergy.pdf python worksheets: 1D Heat Equation,

Dec 14/16  Worksheet 8  Worksheet 8 
Exams
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.
 midterm exam winter 02/03, Solution
 final exam winter 02/03, Solution
 midterm exam winter 04/05, Solution
 final exam winter 04/05, Solution
 exam winter 05/06
 exam winter 06/07
 exam winter 07/08, solution
Literature
Books and Papers
 A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press (in particular Chapter 3,5,6)
 G. Strang: Computational Science and Engineering, WellesleyCambridge Press, 2007
 G. Golub and J. M. Ortega: Scientific Computing and Differential Equations, Academic Press (in particular Chapter 14,8)
 Tveito, Winther: Introduction to Partial Differential Equations  A Computational Approach, Springer, 1998 (in particular Chapter 14,7,10)
 A. Tveito, H.P. Langtangen, B. Frederik Nielsen und X. Cai: Elements of Scientific Computing, Texts in Computational Science and Engineering 7, Springer, 2010 (available as ebook)
 B. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (excellent online material)
 D. Braess: Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics, Cambridge University Press (in particular I.1, I.3, I.4, II.2)
Online Material
 Website for the book of A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science
 Maple Computational Toolbox Files: contains an introduction worksheet to Maple plus several worksheets related to CSE, which are covered in this textbook.
 ODE Software for Matlab (website by J.C. Polking, Rice University)