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

Code	Subject	
MME0001	Differential Equations	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics	2	2+1+1	fundamental	compulsory	
Mathematics and Computer Science	2	2+1+1	fundamental	compulsory	
Applied Mathematics	2	2+1+1	fundamental	compulsory	

Teaching Staff in Charge	Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro
Prof. PETRUSEL Adrian Olimpiu, Ph.D., petrusel@math.ubbcluj.ro
Assoc.Prof. BEGE Antal, Ph.D., bege@math.ubbcluj.ro	
Aims	Introduction to the basic problems of ordinary differential equations (Cauchy problem, boundary value problems) as well as the discussion of some mathematical models governed by differential equations.	
Content	1. Mathematical models governed by differential equations: Mathematical modelling, examples.
2. Differential and integral equations completely solvable.
3. The Cauchy problem: Exiastence, uniqueness and data dependence
4. N-order linear differential equations 
5. First order linear systems of differential equations
6. Dynamical aspects in the theory of differential equations: dynamical systems generated by differential equations, flow anf phase portrait.
7. Stability theory: Stability for linear differentail equations.
	
Bibliography	1. I.A. RUS, Ecuatii diferentiale, ecuatii integrale si sisteme dinamice, Transilvania Press, Cluj, 1996.
2. P. PAVEL, I.A. RUS, Ecuatii diferentiale si integrale, Ed. Did. Ped., Bucuresti, 1975.
3. V. BARBU, Ecuatii diferentiale, Ed. Junimea, Iasi, 1985.
4. D.V. IONESCU, Ecuatii diferentiale si integrale, Ed. Did. Ped., Bucuresti, 1972.
5. L. PERKO, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 2001. 
6. G. MOROSANU, Ecuatii diferentiale. Aplicatii, Ed. Acad., Bucuresti, 1990.
7. G. MICULA, P. PAVEL, Ecuatii diferentiale si integrale prin exercitii si probleme, Ed. Dacia, Cluj, 1989.
8. J.C. ROBINSON,  An introduction to ordinary differential equations, Cambridge University Press, Cambridge, 2004.
	
Assessment	Semestrial activity 10% (of the final mark), 
Project laboratory 20%
Written and oral examination (60%).