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
Information engineering
2
2+1+1
compulsory
Teaching Staff in Charge
Prof. PRECUP Radu, Ph.D.,  r.precupmath.ubbcluj.ro
Prof. PETRUSEL Adrian Olimpiu, Ph.D.,  petruselmath.ubbcluj.ro
Lect. 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