t.BA.XXM8.AN3.20HS (Analysis 3)
Module: Analysis 3
This information was generated on: 24 July 2024
No.
t.BA.XXM8.AN3.20HS
Title
Analysis 3
Organised by
T IAMP
Credits
4

### Description

Version: 4.0 start 01 August 2024

#### Short description

In this module, students learn about linear ordinary differential equations and systems of first-order ODEs. In addition, the basic properties and calculus of functions of several variables are discussed. Moreover, the basic concepts of Fourier analysis are explained and applied to examples.

#### Module coordinator

Henrici Andreas (henr)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels You are able to decide for a given ODE, whether it is linear or not, and whether there exist analytical solution methods. F, M K2 You know methods for solving linear ODE’s with constant coefficients of arbitrary order and systems of first-order ODE’s, and you are able to apply these methods to examples. F, M K3 You are acquainted with functions of several variables, in particular with the various ways of representing these functions. F, M K2, K3 You are acquainted with the important notions and concepts concerning the derivative of functions of several variables, in particular partial derivatives, gradient, directional derivative and Jacobi / Hesse matrix. F, M K2, K3 You know methods for solving extreme value problems in functions of several variables and are able to apply these methods to examples. F, M K2, K3 You know the concept and the significance of multiple integrals, and you know the most important methods for computing such integrals, and you are able to apply these methods to examples. F, M K2, K3 You know the basic concepts of Fourier analysis, and you know the methods for the computation of Fourier series as well as continuous and discrete Fourier transforms, and can apply these methods to examples. F, M K2, K3

#### Module contents

Ordinary differential equations:
• Linear ODE‘s of arbitrary order (2 SW)
• Systems of linear ODE‘s (2 SW)
Calculus of functions of several variables:
• Functions of several variables: Basics (1 SW)
• Partial differentiation, tangent plane, gradient, directional derivative, Jacobi/Hesse matrix (1-2 SW)
• Extreme value problems without/with side condition (1-2 SW)
• Multiple integrals with applications (2 SW)
Fourier analysis:
• Fourier series (1-2 SW)
• Fourier transform (1 SW)
• Discrete Fourier transform (1-2 SW)

#### Teaching materials

provided by the lecturer

#### Supplementary literature

Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler

#### Prerequisites

• Analysis 1,2
• Linear Algebra 1,2

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 3a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester t.b.a. written or online t.b.a. grade max. 20% End-of-semester exam Exam written 90 min grade min. 80%

#### 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.

### Note

Course: Analysis 3 - Praktikum
No.
t.BA.XXM8.AN3.20HS.P
Title
Analysis 3 - Praktikum

### Note

• No module description is available in the system for the cut-off date of 02 August 2099.
Course: Analysis 3 - Vorlesung
No.
t.BA.XXM8.AN3.20HS.V
Title
Analysis 3 - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 02 August 2099.