## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-14-11-K-3

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

## Basedata

SWS 4V+2U 9.0 CP = 270 h 1 Sem. in WiSe  Bachelor (Core) [DE] German Damm, Tobias, Prof. Dr. (PROF | DEPT: MAT) Klar, Axel, Prof. Dr. (PROF | DEPT: MAT) Pinnau, René, Prof. Dr. (PROF | DEPT: MAT) Simeon, Bernd, Prof. Dr. (PROF | DEPT: MAT) + further Lecturers of the department Mathematics [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## Notice

The course is accompanied by a programming lab course [MAT-14-11P-K-3].

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 83210 ("Exercise Class Introduction to Numerical Methods")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

The basic concepts and algorithms for the numerical solution of problems from Analysis and Linear Algebra are covered:
• approximation theory, interpolation of continuous and differentiable functions by polynomials or spline functions
• numerical integration: interpolation and Gaussian quadrature,
• numerical methods for linear systems of equations: Gauss elimination, Cholesky method, QR decomposition, perturbation theory,
• linear curve fitting,
• non-linear and parameter-dependent systems of equations,
• eigenvalue problems.

## Competencies / intended learning achievements

The students know the basic methods and algorithms for the numerical solution of problems in linear algebra and analysis. They are able to critically assess the possibilities and limits of the use of numerical algorithms and are able to work on smaller problems from science and technology using numerical methods.

## Literature

• P. Deuflhard, A. Hohmann: Numerische Mathematik I,
• J. Stoer, R. Bulirsch: Numerische Mathematik,
• J. Werner: Numerische Mathematik.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

## References to Course [MAT-14-11-K-3]

Module Name Context
[MAT-14-00_ERW-M-3] Mathematics as a Potential for Solving Problems A: Modelling and Applied Mathematics WP: Obligation to choose in Obligatory-Modulteil #B (Praktische Mathematik) 4V+2U, 9.0 LP
[MAT-14-10L-M-3] Topic Module B: Mathematics as an Interdisciplinary Cross-Sectional Science WP: Obligation to choose 4V+2U, 9.0 LP
[MAT-14-11-M-3] Introduction to Numerical Methods P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-14-KPOOL-3] Practical Mathematics (B.Sc. Mathematics)