t.BA.XXM5.AN3.19HS (Analysis 3) 
Module: Analysis 3
This information was generated on: 27 September 2021
No.
t.BA.XXM5.AN3.19HS
Title
Analysis 3
Organised by
T ICP
Credits
4

Description

Version: 1.0 start 01 August 2020
 

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 you get an introduction to the (continuous) Fourier transform, and you 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 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 (including coordinate transforms) 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 several 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 can determine the order of an ordinary differential equation, and you can decide whether it is separable or linear. F, M K2, K3
You know analytical methods for the solution of separable and linear first order ordinary differential equations, and you can use these methods on examples. F, M K2, K3
You know analytical methods for the solution 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 transform a linear ordinary differential equation with constant coefficients into an algebraic equation using the Fourier transform. F, M K2, K3

Module contents

 Functions of several variables
  • definition and visualization
  • continuity, differentiability
  • partial derivatives, differential operators, coordinate transforms
  • integral calculus, coordinate transforms
  • divergence theorem, Stokes' theorem, balance equations, scalar potentials for gradient fields
(Continuous) Fourier transform
  • definitions, tables
  • Fourier series for periodic functions
Ordinary differential equations
  • order of an ordinary differential equation, separability, linearity
  • separation of variables and variation of parameters for first order ordinary differential equations
  • analytical solution methods for autonomous and linear second order ordinary differential equations
  • applications of the Fourier transform to linear ordinary differential equations with constant coefficients

Teaching materials

 depending on the lecturer

Supplementary literature

 tba

Prerequisites

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

Teaching language

 (X) German ( ) English

Part of International Profile

 ( ) Yes (X) No

Module structure

 Type 3a
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025

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 max. 20% each
End-of-semester exam exam written 90 minutes grade min. 60%

Remarks

  

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: 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.