401-0663-00L  Numerical Methods for CSE

SemesterHerbstsemester 2016
DozierendeR. Hiptmair
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungThe course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The course focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods in C++.
Lernziel* Knowledge of the fundamental algorithms in numerical mathematics
* Knowledge of the essential terms in numerical mathematics and the
techniques used for the analysis of numerical algorithms
* Ability to choose the appropriate numerical method for concrete problems
* Ability to interpret numerical results
* Ability to implement numerical algorithms afficiently
Inhalt1. Direct Methods for linear systems of equations
2. Least Squares Techniques
3. Data Interpolation and Fitting
4. Filtering Algorithms
8. Approximation of Functions
9. Numerical Quadrature
10. Iterative Methods for non-linear systems of equations
11. Single Step Methods for ODEs
12. Stiff Integrators
SkriptLecture materials (PDF documents and codes) will be made available to participants:

Lecture document: https://people.math.ethz.ch/~grsam/HS16/NumCSE/NumCSE16.pdf

Lecture Git repository: https://gitlab.math.ethz.ch/NumCSE/NumCSE

Tablet classroom notes: http://www.sam.math.ethz.ch/~grsam/HS16/NumCSE/NCSE16_Notes/

Lecture recording: http://www.video.ethz.ch/lectures/d-math/2016/autumn/401-0663-00L.html

Homework problems: https://people.math.ethz.ch/~grsam/HS16/NumCSE/NCSEProblems.pdf
LiteraturU. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011.

A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000.

W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006.

M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002

P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002
Voraussetzungen / BesonderesThe course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Familiarity with C++, object oriented and generic programming is an advantage. Participants of the course are expected to learn C++ by themselves.