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Syllabus for

Academic year
TMV206 - Linear algebra  
Linjär algebra
 
Syllabus adopted 2021-02-26 by Head of Programme (or corresponding)
Owner: TKITE
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Main field of study: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 52126
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 6,0 c Grading: TH   6,0 c   18 Mar 2022 pm J,  09 Jun 2022 pm J,  22 Aug 2022 pm J
0207 Laboratory 1,5 c Grading: UG   1,5 c    

In programs

TKITE SOFTWARE ENGINEERING, Year 1 (compulsory)

Examiner:

Mattias Lennartsson

  Go to Course Homepage


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.

Aim

This course, together with other compulsory mathematics courses, gives general knowledge in mathematics useful in further studies and for the practising engineer.
Linear equations or systems of these appear in all linear models in science, engineering and economy (numerical equations, differntial equations, etc).
Linear algebra provides a common powerful formalism for all such equations.
This course covers the fundamental concepts in linear algebra. MatLab is used as an example of mathematical software used in the analysis of linear problems.

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

  • explain the significance of basic concepts of linear algebra and the connections between them
  • combine prior knowledge of mathematics and various concepts in linear algebra for practical problem solving
  • present solutions to mathematical problems in writing
  • supported by literature and the Internet solve problems that expand and deepen the student's knowledge in linear algebra
  • use the mathematical software Matlab to support calculations
  • write and document programs in Matlab for solving problems in linear algebra

Content

Geometrical Vectors :
Dot product, cross product, linear combinations, orthogonal projection, coordinate systems, lines and planes.
Matrix Algebra :
Addition, multiplication, transpose, identity and inverse.
Linear transformations :
Matrix representation, geometrical mappings, composition and inverse.
Vectors in arbitrary dimension :
Generalization of the geometric concepts to arbitrary dimension.
Linear Equations :
Matrixrepresentation, solution sets, Gaussian elimination and least squares solution.
Determinant :
Definition, computation and geometric interpretation.
Bases and linear independence :
Changing the base of coordinate systems and linear transformations, orthonormal basis and orthogonal matrices.
Eigenvalues ​​and eigenvectors :
Characteristic equation, spectral theorm, diagonalization and the power method.
Graphs and grannmatriser :
Graf concepts, transition matrices, random walks, stationary distribution and Markov chains.

Organisation

The course consists of lectures, exercises and also group exercises that combine theoretical and computer exercises.

More detailed information is given on the course homepage before the start of the course.

Literature

See course homepage.

Examination including compulsory elements

The part Examination is examined through a written exam with grades U, 3, 4 and 5. The part Laboratory is examined through homework assignments.



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.


Page manager Published: Thu 03 Nov 2022.