Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Calculatoare şi tehnologia informaţiei
Programul de studii: Ingineria informatiei - in limba engleza
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MME0001	Differential Equations	

Semester	Hours: C+S+L+P	Category	Status	
2	2+1+1+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
BUICA Adriana	Ph.D.	Assoc.Prof.	Applied Mathematics	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Introduction to the basic problems of ordinary differential equations as well as the discussion of some mathematical models governed by differential equations.	

IV. Course contents
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.

V. 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. 

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Semestrial activity 10% (of the final mark), 
Project laboratory 20%
Contro paper 10%
Written examination (50%).	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. BUICA Adriana, Ph.D.