t.BA.XXM5.LA2.19HS (Linear Algebra 2) 
Module: Linear Algebra 2
This information was generated on: 27 September 2021
No.
t.BA.XXM5.LA2.19HS
Title
Linear Algebra 2
Organised by
T ICP
Credits
4

Description

Version: 2.0 start 01 February 2019
 

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
and the discrete Fourier transform as an application of this concept.

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.
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.
F, M K2, K3

You are able to identify and to solve linear ordinary differential
equations with constant coefficients.

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
  • Orthonormal bases of vector spaces

  • Fourier Series and Discrete Fourier Transform


    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

  • Symmetric und orthogonal 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, Tafeln, Begriffe (Mathematik, Physik, Chemie),
    Orell Füssli Verlag,
    ISBN 978-3-280-04059-1

Prerequisites

  • Knowledge of mathematics of the „technische Berufsmaturität“

  • Knowledge of linear algebra 1 for ET/ST

Teaching language

(X) German ( ) English

Part of International Profile

( ) Yes (X) No

Module structure

Type 2b
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025

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%

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: 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.