Course syllabus
Linjär algebra
Linear Algebra
FMAB20, 6 credits, G1 (First Cycle)
Valid for: 2020/21
Decided by: PLED F/Pi
Date of Decision: 2020-04-01
General Information
Main field: Technology.
Compulsory for: BI1, BME1, C1, D1, E1, F1, I1, L1, M1, MD1, N1, Pi1, V1
Language of instruction: The course will be given in Swedish
Aim
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.
Learning outcomes
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.
Contents
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.
Examination details
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.
Admission
The number of participants is limited to: No
The course overlaps following course/s: FMA421, FMA656, FMA425, FMAA20, FMA420, FMAA55
Reading list
- 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.
Contact and other information
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/