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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.

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.