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

Supplementary literature

  

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 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.