Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Dynamic systems in the light of linear algebra (17.DOM62)

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

General information:

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

To enable students to think abstractly and acquire knowledge in dynamic systems applying linear algebra. The aim of this course is to develop a special way of thinking by using principles of the dynamic systems applying linear algebra. The knowledge they gain is a basis for a better understanding other professional courses and for a successful continuation in studies.

Student is competent to utilize mathematic models of linear algebra in dynamic system in practical work and further education. Knowledge they have acquired, students learn to apply methods gained on this course and to choose algorithms for solving future problems in professional field.

Linear dynamical systems invariant in time. Nonlinear dynamical systems invariant in time. Transitional behavior. Robust stability. Pseudospectrum matrix. Localization of the pseudo-spectrum. Robust matrix dimensions. Discrete Dynamic Systems. Applications in Engineering.

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.

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