Subject: Differential Equations	Code: MME0001	

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

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.	
Selective References	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%)