Course syllabus for Linear algebra

Course syllabus adopted 2023-02-14 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra
  • CodeTMV186
  • Credits7.5 Credits
  • OwnerTKDES
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 56126
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0107 Examination 7.5 c
Grading: TH		 7.5 c
  • 16 Mar 2024 pm J
  • 05 Jun 2024 pm J
  • 29 Aug 2024 pm J

In programmes

Examiner

Go to coursepage (Opens in new tab)

Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

TMV176 or equal (including MATLAB).

Aim

The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics required in further studies as well as in the future professional career.

Learning outcomes (after completion of the course the student should be able to)

  • account for the basic concepts of linear aglebra. 
  • understand and describe the connections between these concepts. 
  • use and combine different concepts in problem solving. 
  • use computer tools in problem solving.

Content

  • Matrix algebra 
  • Matrix inversion and systems of linear equations. 
  • Determinants, the rank of a matrix and systems of linear equations. 
  • Vector spaces, the Euclidean vector space Rn, subspaces, linear independence, basis, dimension, coordinates, change of basis.
  • Linear transformations: matrix representation, applications to rotations, reflections and projections. 
  • Transformations from Rn to Rm .
  • Null space (kernel), column space (range), the rank (dimension) theorem. 
  • Numerical solution of systems of equations: matrix norms, condition number, LU-factorization.
  • The least squares method. 
  • Eigenvalues, eigenvectors and diagonalization. 
  • The power method
  • QR-factorization
  • Problem solving with computational tools

Organisation

Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

Mandatory computer labs that are presented during the course. 
Written exam at the end of the course which has the grading scale U,3,4,5. 
For a passing grade on the course, a passing grade is required on all computer labs and on the written exam. The final grade will be the same as the grade on the exam. 

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.