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t.BA.XXM5.LA1.19HS (Linear Algebra 1)

Module: Linear Algebra 1

This information was generated on: 27 September 2021

No.

t.BA.XXM5.LA1.19HS

Title

Linear Algebra 1

Organised by

T ICP

Credits

4

Description

Version: 2.0 start 01 February 2019

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 and youare able to use them among other things for the description of alternating electrical currents.

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 Numbersand 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 formof complex numbers (polar coordinates, modulus and argument)

Geometric Calculus

Vectors in R^2 and R^3

Norm of a vector, inner productand angle between vectors

Orthogonal Projection

Parametric representations of lines and planes in R^3

Cross Product of vectors

Matrix Calculus

Matrizen, Matrixprodukt

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

LU decomposition

Linear least squares

Inverse Matrix

Determinant

Complex Numbers

Euler‘s formula and exponential form of complex numbers

Exponential and powersof complex numbers

Application of complex numbers to AC current.

Graphical representation of complex functions (Nyquist and Bode plots)

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 1 - Vorlesung

No.

t.BA.XXM5.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.