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t.BA.XXM5.AN3.19HS (Analysis 3)
Module: Analysis 3
This information was generated on: 29 July 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.