Short description

In this course, students learn the basic tools of linear algebra. These include vector and matrix calculus and the solution of linear equation systems. You also learn how to calculate with complex numbers and to use them in a number of applications.

Module coordinator

Schmid Matthias (scmi) 
Learning objectives (competencies)

Objectives 
Competences 
Taxonomy levels 
You know complex numbers and their arithmetic operations in their various representations.

F, M 
K2, K3 
You are familiar with geometric calculus. You are
able to compute norm, inner products, orthogonal
projection, and cross product of vectors and use
vectors to describe geometric objects.

F, M 
K2, K3 
You are able to recognize systems of linear equations and use suitable methods to solve them. In addition, you can apply the linear least square method to overdetermined systems of linear equations.

F, M 
K2, K3 
You are familiar with the basic operations of matrix calculus.
These include the calculation of matrix products, determinants,
inverse matrices, etc

F, M 
K2, K3 

Module contents

Real Numbers and Introduction to Complex Numbers

Number sets: real numbers and field axioms

Complex numbers and the complex plane

Calculus with complex numbers (summation and multiplication)

Polar form of complex numbers (polar coordinates, modulus and argument)

Euler‘s formula and exponential form of complex numbers

Powers and roots of complex numbers
Vector Calculus

Vectors in R^2 and R^3

Norm of a vector, inner product and angle between vectors

Orthogonal Projection

Parametric representations of lines and planes in R^3

Cross Product of vectors
Matrix Calculus

Matrices and matrix product

Solution of systems of linear equations, Gauss elimination and row echelon form

LU decomposition

Linear least squares

Inverse Matrix

Determinant

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/10.1007/9783834823793

Lineare Algebra für Naturwissenschaftler und Ingenieure,
Michael Ruhrländer,
Pearson Studium
ISBN 9783868942712

Formeln, Tabellen, Begriffe
Mathematik  Physik  Chemie
Orell Füssli Verlag,
ISBN 9783280040294

Prerequisites

Knowledge of mathematics of the "technische Berufsmaturität" 
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% 
Endofsemester 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. 