Study Guide@lith
 

Linköping Institute of Technology

 
 
Valid for year : 2017
 
TNA002 Linear Algebra, 6 ECTS credits.
/Linjär algebra/

For:   ED   KTS   MT  

 

Prel. scheduled hours: 87
Rec. self-study hours: 73

  Area of Education: Science

Main field of studies: Mathematics, Applied 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.
  • carry out inspections of results and partial results, in order to verify that these are correct or reasonable
  • solve system of linear ordinary differential equations


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

    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. Distance and approximation. System of linear ordinary differential equations

    Course literature:
    Compendium

    Examination:
    Written examination
    Optional written test
    Individual assignmnet
    Optional written test
    6 ECTS
    0 ECTS
    0 ECTS
    0 ECTS
     



    Course language is Swedish.
    Department offering the course: ITN.
    Director of Studies: George Baravdish
    Examiner: George Baravdish
    Link to the course homepage at the department


    Course Syllabus in Swedish

    Linköping Institute of Technology

     


    Contact: TFK , val@tfk.liu.se
    Last updated: 12/08/2014