Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Dynamical systems in the light of linear algebra 1 (17.DOM61)

Native organizations units: No data

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Mathematics in Engineering (Godina: 2, Winter)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	10

Educational goal:

To enable students to think abstractly and to apply knowledge acquired in linear algebra.

Educational outcome:

Student is competent to use mathematical models and methods of linear algebra in practical work and further education.

Course content:

Dynamical system. Trajectories. Equilibrium state. Linear and nonlinear dynamical systems. Continual and discrete dynamical systems. Dynamical systems invariant in time. Stability. Reactivity. Spectrum of a matrix. Localization of spectrum. Matrix measures. Applications in engineering.

Teaching methods:

Lectures. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
D. Hinrichsen, A.J. Pritchard	Mathematical Systems Theory I. Modelling, State Space Analysis, Stability and Robustness	2005	Springer	English
R. S. Varga	Geršgorin and His Circles	2004	Springer	English
N. Trefethen, M. Embree	Spectra and Pseudospectra. The Behaviour of Nonnormal Matrices and Operators	2005	Princeton University Press	Serbian language
Y. Saad	Iterative Methods for Sparse Linear Systems	2003	SIAM	English
S.K. Godunov	Modern Aspects of Linear Algebra. Translations of Mathematical Monographs	1997	American Mathematical Society	English
R.A. Horn and Charles R. Johnson	Matrix Analysis	1999	Cambridge University Press	English
A.M. Stuart, A.R. Humphries	Dynamical Systems and Numerical Analysis, Cambridge Mongraphs on Applied and Computational Mathematics	1998	Cambridge University Press	English