Linear Algebra with Geometry, 6 credits (TATA67)

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

TEN1	Written examination	U, 3, 4, 5	6 credits
KTR1	Optional written test	U, G	0 credits

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Jan Åslund

Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

Education components

Preliminary scheduled hours: 90 h
Recommended self-study hours: 70 h

Course literature

Linjär algebra med geometri, andra upplagan av L Andersson m fl