t.BA.XXM5.LA2.19HS (Linear Algebra 2)
Module: Linear Algebra 2
This information was generated on: 22 March 2023
No.
t.BA.XXM5.LA2.19HS
Title
Linear Algebra 2
Organised by
T ICP
Credits
4

Description

Version: 3.0 start 01 February 2022

Short description

```Students are familiarised with vector spaces, linear mappings, eigenvalues and eigenvectors. They learn how to mathematically describe linear mappings on vector spaces, using vectors and matrices, and apply these concepts to Fourier analysis and to the solution of linear differential equations.
```

Module coordinator

Schmid Matthias (scmi)

Learning objectives (competencies)

 Objectives Competences Taxonomy levels You are familiar with the abstract notion of a vector space and its subspaces. You can describe vectors as coordinate vectors with respect to some basis. In particular, you know the Fourier series as an application of this concept. p { margin-bottom: 0.1in; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; }p.western { font-family: "Arial", serif; font-size: 10pt; }p.cjk { font-family: "Calibri"; font-size: 10pt; }p.ctl { font-family: "Arial"; font-size: 18pt; F, M K2, K3 ```You are familiar with linear mappings between vector spaces and you are able to describe them with respect to arbitrary bases using matrices and vectors.``` pre { margin-top: 0.08in; margin-bottom: 0.08in; direction: ltr; color: rgb(0, 0, 10); text-align: left; }pre.western { font-family: "Arial", serif; }pre.cjk { font-family: "Calibri"; }pre.ctl { font-family: "Arial"; font-size: 18pt; }p { margin-bottom: 0.1in; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; }p.western { font-family: "Arial", serif; font-size: 10pt; }p.cjk { font-family: "Calibri"; font-size: 10pt; }p.ctl { font-family: "Arial"; font-size: 18pt; } F, M K2, K3 ```You can calculate eigenvalues and eigenvectors of linear mappings and examine matrices for their diagonalizability. You are able to apply the diagonalization of matrices as an important practical insight from linear algebra to technical contexts.``` pre { margin-top: 0.08in; margin-bottom: 0.08in; direction: ltr; color: rgb(0, 0, 10); text-align: left; }pre.western { font-family: "Arial", serif; }pre.cjk { font-family: "Calibri"; }pre.ctl { font-family: "Arial"; font-size: 18pt; }p { margin-bottom: 0.1in; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; }p.western { font-family: "Arial", serif; font-size: 10pt; }p.cjk { font-family: "Calibri"; font-size: 10pt; }p.ctl { font-family: "Arial"; font-size: 18pt; } F, M K2, K3 You are able to identify and to solve linear ordinary differential equations with constant coefficients. p { margin-bottom: 0.1in; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; }p.western { font-family: "Arial", serif; font-size: 10pt; }p.cjk { font-family: "Calibri"; font-size: 10pt; }p.ctl { font-family: "Arial"; font-size: 18pt; F, M K2, K3

Module contents

Vector Spaces

• Vector spaces and vector space axioms

• Subspaces

• Linear independence of vectors
• Basis and dimension of vector spaces
• Inner product, norm and orthonormal bases of vector spaces

• Fourier Series

Linear Mappings

• Linear Mappings

• Examples of linear mappings (reflections, scalings, rotations and projections)

• Fundamental spaces of a matrix (null space and column space)

• Invertible linear mappings (isomorphisms)

• Change of basis of a vector space

Eigenvalues and Eigenvectors

• Calculation of eigenvalues and eigenvectors

• Basis of eigenvectors and diagonalization of matrices

• Linear ordinary differential equations with constant coefficients

Teaching materials

Depending on the lecturer

Supplementary literature

• Lernbuch Lineare Algebra und Analytische Geometrie,
Gerd Fischer, Florian Quiring,

Springer Spektrum Verlag, 2. Auflage
http://dx.doi.org/10.1007/978-3-8348-2379-3

• Lineare Algebra für Naturwissenschaftler und Ingenieure,
Michael Ruhrländer,
Pearson Studium
ISBN 978-3-86894-271-2

• Formeln, Tabellen, Begriffe (Mathematik, Physik, Chemie),
Orell Füssli Verlag,
ISBN 978-3-280-04193-2

Prerequisites

• Knowledge of mathematics of the „technische Berufsmaturität“

• Knowledge of linear algebra 1 for ET/ST

Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 2b

Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester In consultation written or orally Grade 20% End-of-semester exam Exam written 120 min Grade 80%

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: Lineare Algebra 2 - Vorlesung
No.
t.BA.XXM5.LA2.19HS.V
Title
Lineare Algebra 2 - Vorlesung

Note

• No module description is available in the system for the cut-off date of 01 August 2099.