Course syllabus

# Linjär algebra

Linear Algebra

## FMAB20, 6 credits, G1 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Linear Algebra

Valid for: 2022/23

Faculty: Faculty of Engineering, LTH

Decided by: PLED F/Pi

Date of Decision: 2022-04-20

Main field: Technology.

Compulsory for: BI1, BME1, D1, E1, F1, I1, L1, M1, MD1, N1, Pi1, V1

Language of instruction: The course will be given in Swedish

The aim of the course is to give a basic introduction to linear algebra. Particular emphasis is put on the role which this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies in mathematics as well as other subjects. The aim is furthermore to develop the students' ability to solve problems and to assimilate mathematical text.

Knowledge and understanding

For a passing grade the student must

- with confidence be able to solve linear systems of equations and be able to demonstrate an ability to geometrically interpret the solutions of such systems.
- be able to represent, handle and compute with basic geometrical objects in three dimensions, such as points, vectors, lines and planes.
- be able to show a general understanding of the matrix concept and of its coupling to the concept of a linear transformation, and be able to carrry out elementary matrix operations and to solve matrix equations.
- be able to explain the contents of some central definitions, theorems and proofs.

Competences and skills

For a passing grade the student must

- be able to demonstrate a good ability to carry out algebraic calculations within in the framework of the course.
- in connection with problem solving, be able to demonstrate an ability to independently choose and use mathematical methods within linear algebra.
- in connection with problem solving, be able to demonstrate an ability to integrate concepts from the different parts of the course.
- be able to demonstrate an ability to explain mathematical reasoning in a structured and logically clear way.

Systems of linear equations.

Vectors. Bases and coordinate systems. Equations for lines and planes in space. Scalar product with applications. Vector product with applications.

Matrices. Rank. Linear transformations. Determinants. Eigenvalues and eigenvectors. The method of least squares. Linear spaces and subspaces.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written test comprising theory and problems.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

The number of participants is limited to: No

The course overlaps following course/s: FMA421, FMA656, FMA425, FMAA20, FMA420, FMAA55, FMAA21

- Andersson, K G: Lineär algebra. Studentlitteratur, 2000, ISBN: 978-91-44-01608-5. Second edition. Used by the programmes F, I and Pi.
- Extramaterial. Study guide with supplementary exercises. Distributed by the department.
- Månsson, J & Nordbeck, P: Övningar i Linjär algebra. Studentlitteratur, 2019, ISBN: 978-91-44-13355-3. Used by the programmes Bi, BME, C, D, E, L, M, MD, N and V.
- Månsson, J & Nordbeck, P: Linjär algebra. Studentlitteratur, 2019, ISBN: 978-91-44-12740-8. Used by the programmes Bi, BME, C, D, E, L, M, MD, N and V.

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se

Course administrator: Studerandeexpeditionen, expedition@math.lth.se

Course homepage: http://www.maths.lth.se/course/linalgnykod/