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401-0663-00L 7 Credits BSC , MSC D-BSSE , D-INFK
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Numerical Methods for Computer Science

Numerische Methoden für Informatik

Lecturers & Examiners: Dr. Vasile Catrinel Gradinaru
VVZ CR 2.66

Last Updated: 2026-06-01 11:30:50

Abstract

The 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 python.

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 efficiently

Content

0. Numerical computation of integrals 1. Computing with Matrices and Vectors 1.1 Fundamentals 1.2 Software and Libraries 1.4 Computational Effort 1.5 Machine Arithmetic and Consequences 2. Direct Methods for (Square) Linear Systems of Equations 2.1 Introduction: Linear Systems of Equations 2.3 Gaussian Elimination 2.6 Exploiting Structure when Solving Linear Systems 2.7 Sparse Linear Systems 3. Direct Methods for Linear Least Squares Problems 3.1 Least Squares Solution Concepts 3.2 Normal Equation Methods 3.3 Orthogonal Transformation Methods 3.3.1 Transformation Idea 3.3.2 Orthogonal/Unitary Matrices 3.3.3 QR-Decomposition 3.3.4 QR-Based Solver for Linear Least Squares Problems 3.4 Singular Value Decomposition 4. Filtering Algorithms 4.1 Filters and Convolutions 4.2 Discrete Fourier Transform (DFT) 4.3 Fast Fourier Transform (FFT) 5. Data Interpolation and Data Fitting in 1D 5.1 Abstract Interpolation (AI) 5.2 Global Polynomial Interpolation 6. Iterative Methods for Non-Linear Systems of Equations 8.1 Introduction 8.2 Iterative Methods 8.3 Fixed-Point Iterations 8.4 Finding Zeros of Scalar Functions 8.5 Newton’s Method in Rn 8.6. Quasi-Newton Method

Resources

Lecture Notes

Important: python + numpy+ scipy + matplotlib + sympy = learning by doing. Please consult before the start:https://lec.inf.ethz.ch/tutorials/cpp-to-pyandhttp://www.scipy-lectures.orgLecture materials (PDF documents and codes) will be made available to the participants through the course web page and online repositories. Access information will be communicated in the beginning of the course.

Literature

W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006. W. Gander, M.J. Gander, and F. Kwok "Scientific Computing", Springer 2014. M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002

Learning Materials (Links)

General Information

Language
German
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
Keine.
Digital
The exam takes place on devices provided by ETH Zurich.
Die wöchentlichen Übungen (einschließlich Multiple Choice) sind wichtig. Es werden Lernelemente angeboten. Der Notenbonus von 0.25 Notenpunkten wird gewährt, wenn mehr als 75% der insgesamt verfügbaren „Semesterpunkte“ erreicht werden.

Course Components

Type Title Time & Place Hours
lecture Numerische Methoden für Informatik
  • Mon 08:15-10:00 (HG F 1)
  • Thu 10:15-12:00 (HG F 1)
4 h weekly
exercise Numerische Methoden für Informatik
Groups are selected in myStudies. Mo 10-12 oder Mo 14-16
  • Mon 10:15-12:00 (CLA E 4)
  • Mon 10:15-12:00 (LFW E 13)
  • Mon 10:15-12:00 (ML E 12)
  • Mon 10:15-12:00 (ML H 41.1)
  • Mon 10:15-12:00 (ML J 34.1)
  • Mon 10:15-12:00 (ML J 34.3)
  • Mon 14:15-16:00 (HG E 33.1)
  • Mon 14:15-16:00 (LEE D 105)
  • Mon 14:15-16:00 (LFW B 2)
  • Mon 14:15-16:00 (LFW C 5)
  • Mon 14:15-16:00 (ML F 40)
2 h weekly

Offered In