Linear Algebra with Geometry, 6 credits (TATA67)

Linjär algebra med geometri, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

First cycle

Course type

Programme course

Examiner

Jan Åslund

Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CDPU Design and Product Development, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping o
6CEMM Energy - Environment - Management, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping o
6CMMM Mechanical Engineering, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Design and Product Development, M Sc in Engineering
  • Energy - Environment - Management, M Sc in Engineering
  • Mechanical Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Lycée mathematics and physics (natural sciences or technical programmes).

Intended learning outcomes

To give the basic knowledge of linear algebra that is needed in other courses. After the course the student should be able to:

  • use coordinates, bases, scalar products, and vector products.
  • work with lines, planes and calculate distances.
  • solve systems of linear equations.
  • use vectors in R^n and matrices.
  • use the least squares method.
  • compute determinants and use determinants to investigate existence and uniqueness of solutions to quadratic systems of linear equations and existence of inverse of a matrix.
  • determine the matrix of a linear transformation.
  • use change of basis in order to solve problems.
  • compute eigenvalues and eigenvectors, and describe eigenvalues and eigenvectors of a geometrical linear transformation.
  • cite the spectral theorem.
  • use diagonalisation to solve problems including systems of differential equations, recursive sequences, quadratic forms or powers of matrices.
  • perform calculations and verify that the results are correct.

Course content

Linear systems of equations. Geometrical vectors, straight lines and planes. Matrices. Linear spaces. Euclidean spaces. Determinants. Linear mappings. Eigenvalues and eigenvectors. Symmetric mappings. Quadratic forms. Systems of differential equations.

Teaching and working methods

Teaching is done through lectures and problem classes.
The course runs over the entire autumn semester.

Examination

TEN1Written examinationU, 3, 4, 56 credits
KTR1Optional written testU, G0 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Jan Åslund

Education components

Preliminär schemalagd tid: 90 h
Rekommenderad självstudietid: 70 h

Course literature

Linjär algebra med geometri, andra upplagan av L Andersson m fl
Linjär algebra med geometri, andra upplagan av L Andersson m fl
TEN1 Written examination U, 3, 4, 5 6 credits
KTR1 Optional written test U, G 0 credits

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page. There are no files available for this course.

Page responsible: Info Centre, infocenter@liu.se