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401-0663-00L  Numerical Methods for CSE

SemesterHerbstsemester 2019
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
Inhalt* Computing with Matrices and Vectors
* Direct Methods for linear systems of equations
* Least Squares Techniques
* Data Interpolation and Fitting
[ Filtering Algorithms, optional]
* Approximation of Functions
* Numerical Quadrature
* Iterative Methods for non-linear systems of equations
* Single Step Methods for ODEs
* Stiff Integrators
SkriptLecture materials (PDF documents and codes) will be made available to the participants through the course web page, whose address will be announced in the beginning of the course.
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.

W. Gander, M.J. Gander, and F. Kwok "Scientific Computing", Springer 2014.

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.