## 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 Information engineering 2 2+1+1 fundamental compulsory
 Teaching Staff in Charge
 Prof. PRECUP Radu, Ph.D.,  r.precupmath.ubbcluj.roAssoc.Prof. BUICA Adriana, Ph.D.,  abuicamath.ubbcluj.roLect. ANDRAS Szilard Karoly,  andraszmath.ubbcluj.ro
 Aims Introduction to the basic problems of ordinary differential equations as well as the discussion of some mathematical models governed by differential equations.
 Content 1. Introduction: the notion of differential equation; classification; differential systems; the equivalence of an n-order differential equation to a first order differential system; the initial value problem. 2. Mathematical modelling, examples. 3. First order differential equations completely solvable. 4. The Cauchy problem: Existence, uniqueness and data dependence; succesive approximations; upper and lower solutions; extremal solutions. 5. N-order linear differential equations 6. First order linear systems of differential equations 7. Dynamical aspects in the theory of differential equations: dynamical systems generated by differential equations, flow anf phase portrait. 8. Stability theory: Stability for linear differentail equations.
 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.
 Assessment Semestrial activity 10% (of the final mark), Project laboratory 20% Contro paper 10% Written examination (50%).
 Links: Syllabus for all subjects Romanian version for this subject Rtf format for this subject