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406-0663-AAL 8 Credits MSC D-MATH , D-PHYS

Numerical Methods for CSE

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
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.
VVZ CR n/a

Last Updated: 2026-02-05 15:54:13

Abstract

Introduction 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++

Content

1. 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

Resources

Lecture Notes

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

Literature

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 U. Ascher and C. Greif "A first course in Numerical Methods"

General Information

Language
English
Levels
MSC
Frequency
Semesterly recurring

Examination

Type
session examination
Mode
written 225 minutes
Aids
None
Mode of examination: written 180 minutes (the 225 minutes mentioned elsewhere includes the time reserved for reading the examination).Same exam as for the course unit 401-0663-00L, which is taught during the autumn semester and where a 30-minutes mid-term exam and a 30-minutes end-term exam (both not mandatory) will be held during the teaching period on dates specified in the beginning of the semester. The grades of these interim examinations will be taken into account through a BONUS of up to 20% for the final grade. The bonus can also be acquired by students who must take the performance assessment for the course unit 406-0663-AAL if they take part in the exams during the semester.Computer based examination involving coding problems beside theoretical questions. Parts of the lecture documents and other materials will be made available online during the examination.

Course Components

Type Title Time & Place Hours
revision course / private study Numerical Methods for CSE
Self-study course. No presence required.
No time listed 240 h semesterly

Offered In