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Linköping Institute of Technology

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Valid for year : 2007
 
TNA002 Linear Algebra, 6 ECTS credits.
/Linjär algebra/

For:   ED   ES   KTS   MT  

 

Prel. scheduled hours: 48
Rec. self-study hours: 112

  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, computer graphics, numerical analysis, mathematical statistics, control theory, linear optimization and other subjects. It is also included to develop the ability of using the mathematical language both written and oral. It is necessary for the participant to be able to
  • Solve systems of linear equations
  • Work with inner and cross product
  • Calculate with matrices and determinants
  • Calculate with vectors and coordinates in a vector space
  • Determine the matrix for a linear transformation and the kernel and the range for such matrices
  • Determine ON-basis in an inner product space
  • Do orthogonal projection on subspaces and to use least squares approximations
  • Solve problems by changing basis
  • Determine and to use eigenvalues and eigenvectors in different problems
  • Use the spectral theorem in different problems
  • Determine the canonical basis of quadratic forms and to use these to solve geometrical problems
  • Solve systems of differential equations

  • Prerequisites: (valid for students admitted to programmes within which the course is offered)
    Lycée mathematics and physics (natural sciences or technical programmes).

    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.

    Organisation:
    The course is given in the form of lectures and tutorials.

    Course contents:
    Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces. Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Systems of differential equations. Distance and pproximation

    Course literature:
    Will be announced later.

    Examination:
    Written examination
    Individual assignments.
    4 p
    0 p
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    6 ECTS
    0 ECTS
     



    Course language is Swedish.
    Department offering the course: ITN.
    Director of Studies: George Baravdish
    Examiner: George Baravdish


    Linköping Institute of Technology

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    Contact: TFK , val@tfk.liu.se
    Last updated: 02/25/2016