Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MME0002	Dynamical Systems	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	6	2+1+0	speciality	optional	
Computer Science	2	2+1+1	fundamental	compulsory	
Mathematics-Computer Science - in Hungarian	6	2+1+0	speciality	optional	

Teaching Staff in Charge	Lect. SERBAN Marcel Adrian, Ph.D., mserban@math.ubbcluj.ro
Assoc.Prof. BUICA Adriana, Ph.D., abuica@math.ubbcluj.ro
Lect. ANDRAS Szilard Karoly, andrasz@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)
	
Bibliography	Davis Jon H., Differential Equations with MAPLE: an Interactive Approach, Birkhäuser, 2001.
Enns R. H., McGuire G., Nonlinear Physics with Maple for Scientists and Engineers, Birkhäuser, 1997.
Hairer E., Numerical Geometric Integration, Internet course, 1999, http://www.unige.ch/math/folks/hairer/polycop.html
Lynch S., Dynamical Systems with Applications using MATLAB, Birkhäuser, 2004.
Rus I.A., Ecuatii diferentiale, ecuatii integrale si sisteme dinamice, Transilvania Press, 1996.
Trif D., Metode numerice in teoria sistemelor dinamice, Transilvania Press, 1997.	
Assessment	1.Two in-class midterm exams, each worth 20% of course 
2.Lab report, worth 10% of course grade.
3.Final exam, worth 50% of course grade.