t.BA.XXM4.NUM.19HS (Numerics)
Module: Numerics
This information was generated on: 18 May 2024
No.
t.BA.XXM4.NUM.19HS
Title
Numerics
Organised by
T IAMP
Credits
4

### Description

Version: 1.0 start 01 February 2020

#### Short description

Introduction to numerical methods for engineers.

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels Providing the analytical and numerical tools needed in engineering subjects. Introduction to the way of thinking of discrete and numerical mathematics.  To convey the role of applied mathematics in science and technology. You know the terms consistency, convergence, local/global error, error order, stability. You can calculate and visualize both local and global errors for suitable examples. M, F K3 You know important algorithms and numerical parameters for solving linear systems of equations and apply them correctly using examples. M, F K3 You are able to solve linear compensation problems with the help of QR decomposition and know the geometrical interpretation of the normal equation. M, F K3 You can approximate a function using cubic splines. M, F K3 You know common explicit as well as implicit one-step procedures, e.g. procedures according to Euler, Runge, Trapez, classical Runge-Kutta, Heun, and can use them for the approximate solution of initial value problems. M, F K3 You can use finite differences to solve one-dimensional boundary value problems. M, F K3

#### Module contents

• Numerical methods for ordinary differential equations
• One-step procedure
• Discretization error, convergence
• Explicit and implicit numerical methods
• Explicit: Euler, Runge, Heun, classic Runge-Kutta
• Implicit: trapezoid, center point rule
• (optional) 4th order Gauss Legendre
• (optional) Semi-implicit procedures
• (optional) step size control
• Linear equations
• triangular matrices, LR decomposition, Cholesky, tridiagonal matrices
• finite difference method for one-dimensional boundary value problems
• (optional) time dependent boundary value problems
• explicit, implicit Euler method
• Linear least square methods
• Normal equation, Condition
• Cholesky, QR decomposition
• Splines
• Introduction cubic splines
• (optional) B-Splines
• (optional) data fit with (smoothing) B-Splines

#### Teaching materials

script, exercise material

#### Supplementary literature

Wolfgang Dahmen, Arnold Reusken, Numerik für Ingenieure und Naturwissenschaftler, Springer-Lehrbuch

#### Prerequisites

Analysis I - III, Lineare Algebra I & II bzw. Algebra und Statistik I & II

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 3a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester max. zwei Standortbestimmungen Note je max. 20% End-of-semester exam schriftlich 120 Minuten Note min. 60%

#### Remarks

The implementation of numerical methods on the computer is an integral part of the lecture.

#### Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Numerik - Praktikum
No.
t.BA.XXM4.NUM.19HS.P
Title
Numerik - Praktikum

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.
Course: Numerik - Vorlesung
No.
t.BA.XXM4.NUM.19HS.V
Title
Numerik - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.