Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MME0002 | Dynamical Systems |
| Teaching Staff in Charge |
Lect. SERBAN Marcel Adrian, Ph.D., mserban math.ubbcluj.roAssoc.Prof. BUICA Adriana, Ph.D., abuica math.ubbcluj.roLect. ANDRAS Szilard Karoly, andrasz math.ubbcluj.roAssoc.Prof. SÁNDOR Jozsef, Ph.D., jsandor math.ubbcluj.ro |
| Aims |
|
Introduction to the basic problems of dynamical systems and mathematical modeling |
| Content |
|
Introduction (basic terminology, examples, computers and dynamical systems)
Unit I: Discrete and continuous dynamical systems (recurrences and ordinary differential equations as dynamical systems, first order equations, higher order differential equations, existence theorems, general linear ordinary differential equations, boundary value problems) Unit II: Qualitative Analysis (limit sets, singular points, stability theory, invariant sets, Poincaré maps, bifurcation theory) Unit III: Numerical Approach (approximate solutions, numerical stability, continuation, calculation of the bifurcation behavior, chaos) |
| References |
|
1. V. Barbu, Ecuaţii diferenţiale, Junimea, Iaşi, 1985.
2. I. A. Rus, Ecuaţii diferenţiale, ecuaţii integrale şi sisteme dinamice, Transilvania Press, Cluj-Napoca, 1996. 3. M.A. Şerban, Ecuaţii şi sisteme de ecuaţii diferenţiale, Presa Universitară Clujană, 2009. 4. G. Micula, P. Pavel, Ecuaţii diferenţiale şi integrale prin probleme şi exerciţii, Dacia, Cluj-Napoca, 1989 (culegere de probleme). 5. G. Moroşanu, Ecuaţii diferenţiale. Aplicaţii, Ed. Academiei, 1989, (culegere de probleme). 6. D. Trif, Metode numerice în teoria sistemelor dinamice, Transilvania Press, 1997. |
| Assessment |
|
1. A test paper on seminar: 10% from the final grade
2. A test paper on laboratory: 10% from the final grade 3. Final exam: 80% from the final grade. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |