Course syllabus for Linear algebra

Course syllabus adopted 2024-02-13 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra
  • CodeMVE481
  • Credits6 Credits
  • OwnerTKSAM
  • 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 58138
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0124 Laboratory 1.5 c
Grading: UG		0 c0 c1.5 c0 c0 c0 c
0224 Examination 4.5 c
Grading: TH		0 c0 c4.5 c0 c0 c0 c

In programmes

Examiner

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

Introductory course in calculus and Computational mathematics

Aim

The aim of the course is to give, together with other mathematics courses, a general mathematical education which is as useful as possible for further studies and technical professional work. The course shall, in a logical and holistic manner, provide knowledge of linear algebra and differential equations which is necessary for further studies in Civil and Environmental Engineering.

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

- add and subtract vectors in space, both geometrically and analytically using Cartesian coordinates. - define scalar and vector products geometrically and use these concepts to solve geometrical problems such as determining the equation for a line or plane in space and computing the area of a triangle or the volume of a tetrahedron using Cartesian coordinates. - determine the solution set of a system of linear equations by hand using row operations, including the cases where the solution is unique, the solution set is empty or it involves free parameters. - perform the standard operations on matrices, including determination of a matrix inverse by hand when this is computationally feasible - compute the determinant of a square matrix using the usual methods of cofactor expansion and row reduction. - rewrite a system of equations in matrix form and explain the connections between inverse matrix, determinant and the solution set for a square system - linear transforms - solve linear equations systems numerically using numerical software. - implement Euler's method as a function with numerical software. - rewrite a higher order differential equation as a system of first order equations and solve the latter numerically.

Content

- Geometrical vectors and applications.
- Systems of linear equations.
- Matrix algebra, determinants.
- Eigenvalues.
- Orthogonality and Least squares.
- Systems of differential equations.
- Applications with numerical software.

Organisation

The course consists of the following learning activities: Lectures, Tutorials and Computer Labs.

Literature

Communicated at the beginning of the course.

Examination including compulsory elements

In order to pass the course one must:
- Pass the written examination
- Pass the computer labs

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 on educational support due to disability.