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## Syllabus for

TMA841 - Linear algebra

Owner: TKVOV
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish
Block schedule: LA

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0104 Examination 7,5 c Grading: TH 7,5 c 12 Mar 2014 am V, 16 Jan 2014 am V, 25 Aug 2014 am V

#### In programs

TKVOV CIVIL ENGINEERING, Year 1 (compulsory)

#### Examiner:

Bitr professor  Lyudmila Turowska
Bitr professor  Hjalmar Rosengren

#### Replaces

TMA840   Linear algebra

#### Course evaluation:

http://document.chalmers.se/doc/4513b816-d78c-4afe-9ebd-a701872fbc25

#### Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

#### Course specific prerequisites

Introductory course in mathematics

#### 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)

After this 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 the software MATLAB 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 linear equations: Matrix norms,
conditioning numbers, LU-factorization.
The least squares method.
Eigenvalues, eigenvectors and diagonalization.
The power method, QR-factorization. MATLAB applications.

#### 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

More detailed information about the examination will be given on the course web page before start of the course.
Examples of assessments are:
-selected exercises are to be presented to the teacher orally or in writing during the course,
-other documentation of how the student's knowledge develops,
-project work, individually or in group,
-written or oral exam during and/or at the end of the course.

Page manager Published: Thu 03 Nov 2022.