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401-2653-21L 7 Credits BSC D-MATH

Numerical Analysis I

Lecturers & Examiners: Prof. Dr. Christoph Schwab
VVZ CR n/a

Last Updated: 2026-06-03 00:07:54

Abstract

This course gives an introduction to mathematical analysis of numerical methods, aimed at mathematics majors.Prerequisites are 1-year courses on real analysis and linear algebra.The course covers numerical linear algebra, quadrature, interpolation and approximation, and least squares as well as proof techniques and main results on their mathematical error analysis and implementation.

Objective

Knowledge of the fundamental numerical methods, their mathematical foundation as well as `numerical literacy': application of numerical methods, mathematical foundations of numerical methods, and basic mathematical methods of the analysis of stability, consistency and convergence of numerical methods, MATLAB/ Python implementation.

Content

Rounding error analysis, stability, consistency, forward and backward error, direct solution of linear systems of equations, iterative solution of systems of nonlinear equations, interpolation and approximation (polynomial as well as trigonometric), least squares regression, extrapolation, numerical quadrature, elementary optimization methods.

Resources

Lecture Notes

Lecture Notes and reading list will be available.

Literature

Lecture Notes (german or english) will be made available to registered students of ETH BSc MATH. Quarteroni, Sacco and Saleri, Numerische Mathematik 1 + 2, Springer Verlag 2002 (in German). There is an English version of this text, containing both German volumes, from the same publisher. If you feel more comfortable with English, you can follow this text as well. Content and Indexing are identical in the German and the English text.

General Information

Language
English
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
Handwritten summary, 10 pages A4 (no printouts of notes written with an electronic stylus). Dictionaries are not permitted.
Digital
The exam takes place on devices provided by ETH Zurich.
The learning tasks offered during the semester measure active participation in the exercises, which is graded in several stages with up to 0.25 grade points. This bonus of 0 to 0.25 is added unrounded to the unrounded grade from the examination.(In the course Numerical Analysis I, participation is graded by the submission of exercises. Students who have completed at least 2/3 of the exercises in a meaningful way can receive a bonus of a maximum of 0.25 grade points in their final grade. Further details to be confirmed.)The session examination includes theoretical problems (to be completed on paper) and implementation tasks (to be completed in the MATLAB on a computer provided by the ETH).

Course Components

Type Title Time & Place Hours
lecture Numerical Analysis I (Numerische Mathematik I)
This course is offered in English in HS 2026.
No time listed 3 h weekly
exercise Numerical Analysis I (Numerische Mathematik I)
One or two of the exercise groups are conducted in German.All exercise sheets are in English.
No time listed 2 h weekly

Offered In