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t.BA.XXM3.LA1.19HS (Linear Algebra 1)
Module: Linear Algebra 1
This information was generated on: 22 February 2024
No.
t.BA.XXM3.LA1.19HS
Title
Linear Algebra 1
Organised by
T IAMP
Credits
4
Description
Version: 3.0 start 01 August 2019
Short description
Students are familiarised with and master the basic concepts and propositions of linear algebra and analytic geometry. They can formulate simple concrete questions in the mathematical language and are able to solve these independently and present their solutions.
Module coordinator
Landry Chantal (lany)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
You know vectors in two- and three-dimensional space and are familiar with the arithmetic operations of vector geometry.
F, M
K2, K3
You can analytically describe and solve geometric problems of the plane and the space with the help of the vector calculation.
F, M
K2, K3
You are familiar with the matrix calculus and can use it.
F, M
K2, K3
You can formulate linear systems of equations and determine, if these systems are solvable.
F, M
K2, K3
You know algorithms for solving linear systems of equations and can apply them.
F, M
K3
You master the essential properties and calculation rules of the determinants.
F, M
K2
You know algorithms for calculating determinants and can apply them.
F. M
K3
Module contents
Vector geometry:
Definition of free and bound vectors
Vector calculus in two- and three-dimensional space
Applications in analytic geometry (lines and planes)
Matrices:
Definition of a real Matrix and special square matrices
Arithmetic operations on matrices
Invertible matrix
System of linear equations:
Definition of a linear system and its representation using matrices
Solvability of a linear system and rank of a matrix
Solving a linear system: Gaussian elimination, Gauss-Jordan elimination, Cramer's rule
Applications: matrix inversion and evaluating linear independence of a set of vectors
Determinant
Definition of the determinant of a square matrix
Properties and calculation rules of the determinant
Laplace expansion for computing determinants
Applications
Teaching materials
Lecture notes, blackboard sketches, handout
Supplementary literature
Ruhrländer, M.: Lineare Algebra für Naturwissenschaftler und Ingenieure, Pearson Studium
Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler (Bände I und II), Vieweg+Teubner, 12. Auflage
Gramlich, G.M.: Lineare Algebra: Eine Einführung, Carl Hanser Verlag
Prerequisites
Knowledge of mathematics of the technical Berufsmatura
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
at least two assessments
written
Per assessment max. 45 minutes
Grade
count only with a positive contribution to the final module grade with a total of 30%
End-of-semester exam
exam
written
90 min
Grade
Min. 70%
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.
Note
Additional available versions:
1.0 start 01 February 2019
Course: Lineare Algebra 1 - Vorlesung
No.
t.BA.XXM3.LA1.19HS.V
Title
Lineare Algebra 1 - Vorlesung
Note
No module description is available in the system for the cut-off date of 01 August 2099.