406-0663-AAL Numerical Methods for CSE
| Semester | Autumn Semester 2020 |
| Lecturers | R. Hiptmair |
| 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++. |
| Learning 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 | * Direct Methods for linear systems of equations * Least Squares Techniques * Data Interpolation and Fitting * Filtering Algorithms * Approximation of Functions * Numerical Quadrature * Iterative Methods for non-linear systems of equations |
| 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. |