DS1KMF - Kanonske matricne forme i njihove primene u elektrotehnici

Course specification
Course title
Acronym DS1KMF
Study programme Electrical Engineering and Computing
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      ESPB 9.0 Status elective
      Condition Mathematics 1, Mathematics 2
      The goal The aim of the course is to provide students with theoretical and practical knowledge on using the techniques of canonical forms to the related problems in electrical engineering. The complexity of the algorithms for calculating canonical forms (Hermite, Smith, rational and Jordan) is considered. We also discuss their application to different areas of electrical engineering.
      The outcome The outcome of the course is solid mathematical support for the practical application of the canonical form on the problems in some areas of electrical engineering.
      Contents of lectures Rings. Modules. Modules over a Principal ideal Domain. Normal Forms of Matrices (Hermite, Smith, Rational and Jordan). Minimal and Characteristic Polynomials. Eigenvalues and Eigenvectors. Generalized Eigenvectors. Algebraic and Geometric Multiplicities.Invariant Factors. Elementary Divisors. Systems of Linear Differential Equations. Application of canonical matrix form to electrical engineering.
      Contents of exercises The practical part of teaching involves the same teaching units as theoretical contents. We will illustrated mentioned topics by the examples and by using the appropriate mathematical software.
      1. J. Kečkić, Linearna algebra teorija i zadaci, Matematički problemi i ekspozicije 10, Naučna knjiga, Beograd, 1990. (Original title)
      2. D. S. Dummit, R. M. Foote, Abstract Algebra, third edition, Johan Wiley & Sons, Hoboken, 2004. (Original title)
      3. F. P. Gantmaher, Theory of Matrices, Nauka, Moscow, 1988. (Original title)
      4. S. Weintraub, Jordan Canonical Form: Application to Differential Equations, Morgan and Claypool, 2008. (Original title)
      5. S. Weintraub, Jordan Canonical Form: Theory and Practice, Morgan and Claypool 2009. (Original title)
      Number of hours per week during the semester/trimester/year
      Lectures Exercises OTC Study and Research Other classes
      Methods of teaching Formal lecture, practicals ang group work.
      Knowledge score (maximum points 100)
      Pre obligations Points Final exam Points
      Activites during lectures 25 Test paper 50
      Practical lessons Oral examination
      Colloquia 25