406-0663-AAL  Numerical Methods for CSE

SemesterSpring Semester 2021
LecturersR. Hiptmair
Periodicityevery semester recurring course
Language of instructionEnglish
CommentEnrolment 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.


AbstractIntroduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology.
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 in C++
Content1. Computing with Matrices and Vectors
2. Direct Methods for Linear Systems of Equations
3. Direct Methods for Linear Least Squares Problems
4. Filtering Algorithms
5. Data Interpolation and Data Fitting in 1D
6. Approximation of Functions in 1D
7. Numerical Quadrature
8. Iterative Methods for Non-linear Systems of Equations
12. Numerical Integration - Single Step Methods
13. Single Step Methods for Stiff Initial Value Problems
Lecture notesLink
LiteratureW. 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
U. Ascher and C. Greif "A first course in Numerical Methods"
Prerequisites / NoticeExamination will be conducted at the computer and will involve coding in C++/Eigen.
A course covering the material is taught in English every autumn term (course unit 401-0663-00L). Course documents, exercises and examinations are available online.