406-0663-AAL Numerical Methods for CSE
|Semester||Autumn Semester 2016|
|Periodicity||every semester recurring course|
|Language of instruction||English|
|Comment||Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.|
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
|Abstract||he 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++.|
|Objective||* 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
|Content||1. 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
|Lecture notes||Lecture materials (PDF documents and codes) will be made available to participants.|
|Literature||U. 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
|Prerequisites / Notice||Solid knowledge about fundamental concepts and technques from linear algebra & calculus as taught in the first year of science and engineering curricula.|
The 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.