t.BA.XXM6.AN3.19HS (Analysis 3)
Module: Analysis 3
This information was generated on: 22 February 2024
No.
t.BA.XXM6.AN3.19HS
Title
Analysis 3
Organised by
T IAMP
Credits
4

### Description

Version: 3.0 start 01 August 2022

#### Short description

The topics covered by Analysis 3 are calculation with complex numbers and the solution of ODEs, including the Laplace transformation.
In the second part, the focus is on multidimensional analysis and aspects of the vector analysis.

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels You know the basics of the arithmetic of complex numbers and can apply these correct. F, M K2, K3 You can develop periodic functions in Fourier series. F, M K3 You can decide for each ODE if it is linearly and if there exists an analytical solution method. F, M K3 You know the main properties of the Laplace transformation. F, M K3 You know the solution methods for linear ODE with constant coefficients of higher order and can apply these on examples. F, M K3 You are familiar with fundamental forms, notations and properties of multidimensional functions. F, M K2, K3 You are familiar with the main definitions and concepts of the differential calculus of multidimensional functions, particularly with partial derivative, gradient, directional derivative and tangent plane. F, M K3 You can integrate multidimensional functions over general domains. You can transform such integrals in several voordinates. F, M K3 You can calculate the work in a vector field. You can decide, if a vector field is conservativly and calculate the potential if applicable. F, M K3 You know the propositions of Gauss and Stokes and their physical interpretations. F, M K3

#### Module contents

1. Complex numbers

1.1 Gaussian number plane
1.2 Calculating with complex numbers
1.3 The trigonometric form
1.4 The exponential form
1.5 Fourier series

2. Ordinary differential equations (ODEs)

2.1 Fundamentals of ODEs
2.2 Laplace transformation
2.3 Linear ODEs of first order
2.4 Linear ODEs of second order with constant coefficients

3. Differential and integral calculus of multidimensional functions

3.1 Functions in several variables
3.2 Partial differentiation
3.3 Tangent plane, directional derivative and selected applications
3.4 Multidimensional integration in several coordinates

4. Vector analysis

4.1 Scalar and vector fields
4.2 Differential operators - gradient, divergence, rotation
4.3 Curvilinear integrals
4.4 Surface integrals
4.5 Integral propositions of Gauss and Stokes

#### Teaching materials

lecture notes, exercises

#### Supplementary literature

Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler

#### Prerequisites

• Analysis I und II
• Algebra und Statistik I und II

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 3a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester test written 45 min mark 20% End-of-semester exam exam written 90 min mark 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.XXM6.AN3.19HS.P
Title
Analysis 3 - Praktikum

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.
Course: Analysis 3 - Vorlesung
No.
t.BA.XXM6.AN3.19HS.V
Title
Analysis 3 - Vorlesung

### Note

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