401-2673-00L Numerical Methods for CSE

Semester	Autumn Semester 2022
Lecturers	R. Hiptmair
Periodicity	yearly recurring course
Language of instruction	English

Courses

Number

Title

Hours

Lecturers

401-2673-00 V

Numerical Methods for CSE

This course is designed in a flipped classroom format based on video tutorials and supplemented by a weekly question-and-answer session, for which attendance is highly recommended.

2 hrs

Fri/2	13:15-15:00	HG F 1 »
Fri	14:15-16:00	HG F 1 »

R. Hiptmair

401-2673-00 U

Numerical Methods for CSE

2 hrs

Mon	10:15-12:00	LFW B 3 »
	10:15-12:00	ML F 40 »
	10:15-12:00	NO D 11 »

R. Hiptmair

401-2673-00 P

Numerical Methods for CSE

Self-study based on video tutorial and lecture notes.

4 hrs

R. Hiptmair

Catalogue data

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 C++.

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

Content

* Computing with Matrices and Vectors
* Direct Methods for linear systems of equations
* Least Squares Techniques
* Data Interpolation and Fitting
* Iterative Methods for non-linear systems of equations
* Filtering Algorithms
* Approximation of Functions
* Numerical Quadrature

Lecture notes

Lecture materials (PDF documents and codes) will be made available to the participants through the course web page, whose address will be announced in the beginning of the course.

Literature

U. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011.

A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000.

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

Prerequisites / Notice

The course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Knowledge of C++ is taken for granted.

Competencies

Subject-specific Competencies	Concepts and Theories	assessed
	Techniques and Technologies	assessed
Method-specific Competencies	Analytical Competencies	assessed
	Media and Digital Technologies	fostered
	Problem-solving	assessed
	Project Management	fostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
In examination block for	Bachelor's Degree Programme in Computational Science and Engineering 2018; Version 13.12.2022 (Examination Block G1)
ECTS credits	9 credits
Examiners	R. Hiptmair
Type	session examination
Language of examination	English
Repetition	The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination	written 210 minutes
Additional information on mode of examination	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.
Written aids	No aids admitted. Some documentations and documents will be made available on the exam computers.
Online examination	The examination may take place on the computer.
Distance examination	It is not possible to take a distance examination.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding.