t.BA.XXM5.AN3.19HS (Analysis 3) Module: Analysis 3
This information was generated on: 30 November 2023
No.
t.BA.XXM5.AN3.19HS
Title
Analysis 3
Organised by
T ICP
Credits
4

### Description

Version: 2.0 start 01 August 2021

#### Short description

The main topic of this module is the differential and integral calculus of generally vector-valued functions of several real variables. In addition, students are introduced to the (continuous) Fourier transform and learn about analytical methods for the solution of ordinary differential equations.

#### Module coordinator

Kirsch Christoph (kirs)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels You know various definitions of the (continuous) Fourier transform, and you can work with tables of Fourier transform pairs. F, M K2, K3 You can compute Fourier transforms of functions in both directions with the help of tables. You can calculate Fourier series of periodic functions. F, M K2, K3 You know properties such as continuity and differentiability of functions of several variables, and you can visualize these functions appropriately. F, M K2, K3 You can compute partial derivatives of functions. You know the calculation rules for the differential operators gradient, divergence and curl and you can use them on examples. F, M K2, K3 You can integrate functions of several variables over general domains, and you can transform such integrals into arbitrary coordinates. F, M K2, K3 You can formulate balance equations for the state variables of a physical system using the divergence theorem, and you can compute scalar potentials for gradient fields using Stokes' theorem. F, M K2, K3 You know the slope field of a first order ordinary differential equation, and you can derive qualitative properties of the integral curves from it. F, M K2, K3 You know the method of substitution for the solution of special first order ordinary differential equations, and you can use this method on examples. F, M K2, K3 You know analytical methods for the reduction of order of special second order ordinary differential equations, and you can use these methods on examples. F, M K2, K3 You can rewrite arbitrary higher order ordinary differential equations as systems of first order ordinary differential equations. F, M K2, K3 You can solve systems of linear first order ordinary differential equations analytically. F, M K2, K3 You can write initial and boundary value problems with ordinary differential equations in standard form.

#### Module contents

(Continuous) Fourier transform
• definitions, tables
• Fourier series for periodic functions
Functions of several variables
• definition and visualization
• continuity, differentiability
• partial derivatives, differential operators
• integral calculus, coordinate transforms
• divergence theorem, Stokes' theorem, balance equations, scalar potentials for gradient fields
Ordinary differential equations
• slope field and integral curves of ordinary differential equations
• substitution methods for special first order ordinary differential equations
• reduction or order for special second order ordinary differential equations
• solution of systems of linear ordinary differential equations
• initial and boundary value problems with ordinary differential equations

#### Teaching materials

depending on the lecturer

#### Prerequisites

XXM4.AN1, XXM4.AN2, XXM5.LA1, XXM5.LA2

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

type 3a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester depending on the lecturer depending on the lecturer depending on the lecturer grade 20% End-of-semester exam exam written 90 minutes grade 80%

#### Remarks

At least one graded assignment during the semester. Number and weighting of graded assignments equal among all lecturers.

#### 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.XXM5.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.XXM5.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.