Numerical Programming I - Winter 08: Difference between revisions

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{{Lecture
{{Lecture
| term = Winter 08
| term = Winter 08
| lecturer = [[Michael Bader|Dr. Michael Bader]]
| lecturer = [[Univ.-Prof. Dr. Hans-Joachim Bungartz]]
| timeplace = Wednesday, t.b.a., Raum 02.07.023, Beginn: 23.10.2008
| timeplace = Lecture: Tuesday 9:00 - 10:30, lecture room 02.07.023; Thursday 12:00 - 13:30, lecture room 02.07.023
| credits = 2 SWS / 3 Credits
: Tutorial: Monday, 14:15 - 15:45, lecture room 02.07.023
| audience = Computational Science and Engineering, 1. Semester
| credits = 6 SWS (4V + 2Ü) / 8 Credits
| tutorials = -
| audience = Computational Science and Engineering, 1st semester ([https://www.in.tum.de/myintum/kurs_verwaltung/cm.html?cmid=228&lang=en module IN2156])
| exam = written exam (time and day t.b.a.)
| tutorials = [[ Stefanie Schraufstetter]]
| exam = February 19th (see [[#Exam |here]])
}}
}}
= News =
The results of the exam are available now via the mytum-Portal. Fpr details to the exam review and the repeat exam see [[#Exam |here]].
<!--<font color=red>
'''Changes in schedule:'''
* Monday, Jan 26th: lecture (instead of tutorial)
* Tuesday, Jan 27th: tutorial (instead of lecture)
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= Contents =
= Contents =
Line 13: Line 26:
This course provides an overview of numerical algorithms. Topics are:
This course provides an overview of numerical algorithms. Topics are:


    * Floating point arithmetics
* Floating point arithmetics
    * Linear systems
* Solving Linear systems
    * Eigenvalue problems
* Interpolation
    * Interpolation
* Quadrature
    * Quadrature
* Eigenvalue problems
    * Basics of iterative methods
* Basics of iterative methods
    * Basics of numerical methods for ordinary differential equations
* Basics of numerical methods for ordinary differential equations


The course will start with a short revision of mathematical foundations for numerical algorithms.  
The course will start with a short revision of mathematical foundations for numerical algorithms.  


* Foundations of numerical algorithms from calculus and linear algebra
* Floating point arithmetic (rounding error analysis, condition, and stability)
* Solving linear systems (Gaussian elimination, LR-factorization, pivoting, least squares, QR-factorization)
* Interpolation (polynomial ~, Spline ~, trigonometric ~, Fast Fourier Transform)
* Quadrature (Newton-Cotes formulae, extrapolation, Gaussian ~)
* Eigenvalue problems (symmetric, non-symmetric)
* Fundamentals of iterative methods (Jacobi and Gauss-Seidel ~, gradient ~, fixed point iteration, Newton ~)
* Basics of numerical methods for ordinary differential equations (Finite Differences, Euler and Runge-Kutta, consistency and convergence)




= Lecture Notes and Material =
= Lecture Notes =
 
<!-- (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_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_03.pdf Chapter 3:] Interpolation
* [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 (addendum: [http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf Painless CG])
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/slides/handout_08.pdf Chapter 8:] Ordinary Differential Equations
 
 
 
= Tutorial =
 
Here are the sheets for the tutorial:
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_01.pdf Exercise 1:] Mathematical Essentials 
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_02.pdf Exercise 2:] Linear Algebra
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_03.pdf Exercise 3:] Calculus of one Variable
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_04.pdf Exercise 4:] Calculus of Several Variables
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_05.pdf Exercise 5:] Stochastics and Statistics  ([http://www.math.unb.ca/~knight/utility/NormTble.htm Normal Distribution Table])
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_06.pdf Exercise 6:] Floating Point Numbers and Condition
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_07.pdf Exercise 7:] Interpolation I
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_08.pdf Exercise 8:] Interpolation II
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_09.pdf Exercise 9:] Numerical Quadrature
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_10.pdf Exercise 10:] Direct Methods for Solving Linear Systems for Equations
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_11.pdf Exercise 11:] Symmetric Eigenvalue Problem
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_12.pdf Exercise 12:] Iterative Methods: Roots and Optima
* [http://www5.in.tum.de/lehre/vorlesungen/num_prog_cse/ws08/tutorial/exercise_13.pdf Exercise 13:] Ordinary Differential Equations
 


(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)
'''Organization:'''
 
Problems will be available one week before being discussed in the tutorial. Within this time, you should try to solve them either on your own or within a small group. Some of the exercises are marked with a black triangle. These problems are intended to be presented in the tutorial by a student. So you should be able to demonstrate the marked problems at the board. Active participation is crucial for admission to the final exam.
Problems marked with 'P' are programming assignments. Solve this problems with MATLAB. A solution will be demonstrated and discussed in the tutorial.


; Introduction - Scientific Computing as a Discipline : Oct
: [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
: [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
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population.pdf slides]
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/popmodel.mws popmodel.mws]
; Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
: [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]
: 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]
; Numerical Methods for ODE : Nov
: [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]
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/numerics_ode.mws numerics_ode.mws]
; Discrete Models for the Heat Equation : Dec
: [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]
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws]
; 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 =
The written exam will take place on '''February 19th at 10:15''' in the lecture room '''MW 0350''' (mechanical engineering building) and will take 100 minutes.
There will be allowed not more than '''1 hand-written sheet of paper (no copies!) with your own notices (no calculators, no books, no laptops, ...)'''.
The subject matter of the exam contains '''the lecture and the tutorials as well as the programming exercises'''! There will be no test exam.
The best preparation is to repeat the exercise sheets (compute them by yourself once again) and the slides of the lecture ("did I understand it?") and to do the programming exercises (not only to read the code of the solution!). Then, you won't have any problems in the exam.
<!--
If you are <b>not</b> a CSE student, then please register for the exam via email (schraufs@in.tum.de) by the end of January. Registration is closed now!
-->
The results of the exam are available now via the mytum-Portal. Log in with your mytum-account to access your result.
The exam review will be on Thursday, March 19th, 2009, 12:30-13:00 in the room 02.05.011B (next to the seminar room 02.07.023).
The oral repeat exam (only for students who failed the regular exam) will take place on Thursday, Apr 14, 2008 in the afternoon. Please contact Stefanie Schraufstetter as soon as possible for more details if you have not done that yet.


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, Springer-Verlag, part 1 (8. edition 1999) and part 2 (4. edition 2000)
* Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition)
* Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 3. edition 2002
* Dahlquist, Björck: Numerical Methods in Scientific Computing: Volume 1 & 2, SIAM 2008, [http://www.mai.liu.se/~akbjo/NMbook.html http://www.mai.liu.se/~akbjo/NMbook.html]
* Press, Flannery, Teukolsky, Vetterling: [http://www.nr.com/ Numerical Recipes], Cambridge University Press
* Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
* 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


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

Latest revision as of 08:34, 19 March 2009

Term
Winter 08
Lecturer
Univ.-Prof. Dr. Hans-Joachim Bungartz
Time and Place
Lecture: Tuesday 9:00 - 10:30, lecture room 02.07.023; Thursday 12:00 - 13:30, lecture room 02.07.023
Tutorial: Monday, 14:15 - 15:45, lecture room 02.07.023
Audience
Computational Science and Engineering, 1st semester (module IN2156)
Tutorials
Stefanie Schraufstetter
Exam
February 19th (see here)
Semesterwochenstunden / ECTS Credits
6 SWS (4V + 2Ü) / 8 Credits
TUMonline
{{{tumonline}}}



News

The results of the exam are available now via the mytum-Portal. Fpr details to the exam review and the repeat exam see here.


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


Tutorial

Here are the sheets for the tutorial:


Organization:

Problems will be available one week before being discussed in the tutorial. Within this time, you should try to solve them either on your own or within a small group. Some of the exercises are marked with a black triangle. These problems are intended to be presented in the tutorial by a student. So you should be able to demonstrate the marked problems at the board. Active participation is crucial for admission to the final exam. Problems marked with 'P' are programming assignments. Solve this problems with MATLAB. A solution will be demonstrated and discussed in the tutorial.


Exam

The written exam will take place on February 19th at 10:15 in the lecture room MW 0350 (mechanical engineering building) and will take 100 minutes. There will be allowed not more than 1 hand-written sheet of paper (no copies!) with your own notices (no calculators, no books, no laptops, ...).

The subject matter of the exam contains the lecture and the tutorials as well as the programming exercises! There will be no test exam. The best preparation is to repeat the exercise sheets (compute them by yourself once again) and the slides of the lecture ("did I understand it?") and to do the programming exercises (not only to read the code of the solution!). Then, you won't have any problems in the exam.

The results of the exam are available now via the mytum-Portal. Log in with your mytum-account to access your result. The exam review will be on Thursday, March 19th, 2009, 12:30-13:00 in the room 02.05.011B (next to the seminar room 02.07.023).

The oral repeat exam (only for students who failed the regular exam) will take place on Thursday, Apr 14, 2008 in the afternoon. Please contact Stefanie Schraufstetter as soon as possible for more details if you have not done that yet.



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
  • Dahlquist, Björck: Numerical Methods in Scientific Computing: Volume 1 & 2, SIAM 2008, http://www.mai.liu.se/~akbjo/NMbook.html
  • Press, Flannery, Teukolsky, Vetterling: Numerical Recipes, Cambridge University Press
  • Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
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