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Valid for year : 2007
 
TATA24 Linear Algebra, 8 ECTS credits.
/Linjär algebra/

For:   BAS-X   C   D   Fys   IT   Mat   Y   Yi  

 

Prel. scheduled hours: 76
Rec. self-study hours: 137

  Area of Education: Science

Subject area: Mathematics
  Advancement level (G1, G2, A): G1

Aim:
To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, numerical analysis, mathematical statistics, control theory, linear optimisation and other subjects. After completing the course the students will be able to read and understand the linear algebra which is used in other courses within the programme and the linear algebra which can be found in technical articles. In order to handle this it is necessary to be able to
  • solve systems of linear equations and know of the structure of the set of solutions
  • work with inner product and vector product for geometrical vectors
  • perform calculations with matrices and determinants
  • describe the concepts of a vector space and perform calculations with vectors and coordinates
  • describe the concept of a linear mapping, determine the matrix of a linear mapping and calculate the null space and the range
  • project ortogonally on subspaces and use the method of least squares
  • use change of basis in order to solve problems
  • formulate the spectral theorem and use it in order to solve systems of differential equations and systems of difference equations


Prerequisites: (valid for students admitted to programmes within which the course is offered)


Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Supplementary courses:
TATM88 Linear Algebra, honours course, TATM85 Functional Analysis, TANA25 Numerical Methods II.
Organisation:
Teaching is done through lectures and problem classes.
Course contents:
Linear systems of equations. Geometrical vectors, straight lines and planes. Matrices. Linear spaces. Euclidean spaces. Determinants. Linear mappings. Eigenvalues and eigenvectors. Symmetric mappings. Quadratic forms. Systems of differential equations.
Course literature:
Janfalk, U.; Linjär algebra, published by the Department of Mathematics. Additional material published by the Department of Mathematics.
Examination:
Written examination
Written test
 5,5 p
0 p
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8 ECTS
0 ECTS
 


Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Göran Forsling
Examiner: Thomas Karlsson
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 12/11/2007