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

Code	Subject	
MME1011	Differential Equations with Applications	

Section	Sem.	Hours: C+S+L	Category	Type	
Computational Mathematics - in Hungarian	1	2+1+0	speciality	compulsory	
Didactic Mathematics - in Hungarian	1	2+1+0	speciality	compulsory	
Didactic Mathematics - in Hungarian	3	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Lect. ANDRAS Szilard Karoly, andrasz@math.ubbcluj.ro	
Aims	An interdisciplinary introduction to modeling (economical, biological, chemical models) with dynamical systems. The study of stability and chaotic behavior, simulations.

Content	1. Introduction and historical aspects
2. Mathematics and its applications
3. The process of mathematical modelling
4. Discrete and continuous dynamical systems
5. Models for population biology
6. Steady states, stability
7. Autonomous systems, the study of stability
8. Epidemiologic models
9. The Lorenz model and chaotic behavior
10. Traffic simulation on a highway
	
Bibliography	1. RUS, IOAN A. - IANCU, CRACIUN: Modelare matematica, Editura Transilvania, Cluj-Napoca,  2000
2. IANCU, CRACIUN: Modelare matematica. Teme speciale. Ed. Casa Cartii de Stiinta, Cluj-Napoca, 2002
3. MURRAY,J.D.: Mathematical biology, Springer-Verlag, Berlin,1989. vol I+II 
4. ARROWSMITH, Dynamical systems, Differential equations, maps and chaotic behaviour, Chapmann and Hall, 1992
5. ANDRÁS SZILÁRD: Dinamikus rendszerek, Editura didactica si pedagogica, 2008
6. LOUIS G. BIRTA, GILBERT ARBEZ: Modelling and Simulation, Springer, 2007
7. MIKLÓS FARKAS: Dynamical models in biology, Academic Press, 2001
8. D.R. SCHIER, K.T. WALLENIUS: Applied multidisciplinary modeling, Chapman and Hall, 1999
9. D.R. SCHIER, K.T. WALLENIUS: Applied multidisciplinary modeling, 
10. NINO BOCCARA: Modelling complex systems, Springer, 2004

Assessment	Activity (courses and seminars): 30%
Project: 40%
Final exam 30%

If a student&#8217;s absentees is greater than 40% from the number of all activities, the student has to prepare a special presentation (paper) in a subject specified by the professor.