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Cursus: 201500292
201500292
Linear Algebra
Cursus informatie
Cursus201500292
Studiepunten (ECTS)3
CursustypeCursus
VoertaalEngels
Contactpersoondr. J.B. Timmer
E-mailj.b.timmer@utwente.nl
Docenten
Docent
prof.dr.ir. H.J. Broersma
Docent
dr. W. Kern
Docent
T.A. Leonida
Examinator
dr. J.B. Timmer
Contactpersoon van de cursus
dr. J.B. Timmer
Collegejaar2017
Aanvangsblok
1A
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Leerdoelen
The student is able to:
•        work with systems of linear equations, vectors, matrices, subspaces of the n-dimensional real space, and explain the connections between these concepts,
•        work with determinants, eigenvalues, eigenvectors, linear transformations and connect them with the previous concepts.
 
Inhoud
In Linear Algebra we mainly focus on systems of linear equations (linear systems). Many real life situations can be modeled as a linear system. Examples are networks (traffic networks, data networks, electrical networks, etc.), economic models, chemical reactions, cryptography (coding of messages), scheduling, computer graphics, GPS.
Linear Algebra starts with an introduction of linear systems which will be described using a (coefficient-)matrix. We learn how to solve linear systems systematically, using a row reduction technique on the coefficient matrix.
Thereafter, we focus on operations for vectors and matrices, such as addition, multiplication, inverse and transpose. These operations are fundamental in Linear Algebra.
Next, we deal with sets of vectors with very nice properties: subspaces. It turns out that the properties of subspaces tell us a lot about the structure of solution sets of linear systems. Here the concepts of linear combination, linear independence, basis and dimension play an important role.
We also introduce the concept of determinant of a square matrix. We explore its properties and show some interesting interpretations.
Further, we deal with eigenvectors and eigenvalues of a square matrix. These concepts play a crucial role in discrete dynamic systems, which arise in many scientific fields.
Finally, we examine linear transformations and their properties. Some well-known applications in geometry will be treated as well.
Throughout, much emphasis is laid on the relations among the various concepts.
Voorkennis
Some experience with vectors, lines, planes, and systems of linear equations.
DEELNEMENDE OPLEIDING
M-EE
DEELNEMENDE OPLEIDING
M-EMSYS
DEELNEMENDE OPLEIDING
M-ME
DEELNEMENDE OPLEIDING
M-SC
DEELNEMENDE OPLEIDING
M-SET
Verplicht materiaal
Studiemateriaal
Lecture notes (dictaat)
Aanbevolen materiaal
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