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401-2673-AAL 9 Credits MSC D-PHYS , D-MATH
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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 16:22:21

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 210 minutes
Aids
No aids admitted. Some documentations and documents will be made available on the exam computers.
Digital
The exam takes place on devices provided by ETH Zurich.
Mode of examination: written 180 minutes (leading to 210 minutes total exam time when adding the time reserved for reading the exam problems).Computer based examination involving coding problems beside theoretical questions. Parts of the lecture documents and other materials will be made available on the computers during the examination.An optional 30-minutes mid-term and an optional 30-minutes end-term exam will be held during the teaching period. The grades of these interim examinations will be taken into account through a BONUS of up to 30% for the final grade. The dates for the term exams will be communicated in the beginning of the course.

Course Components

Type Title Time & Place Hours
revision course / private study Numerical Methods for CSE
Self-study course. No presence required. Same contents as 401-2673-00L Numerical Methods for CSE in the previous semester.
No time listed 270 h semesterly

Offered In