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	
MMA0002	Mathematical Analysis	

Semester	Hours: C+S+L	Category	Status	
1	3+2+0		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
MURESAN Marian	Ph.D.	Prof.	Mathematical Analysis and Optimization	*			

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

III. Course objectives
Getting know the algebraic and  topological structure of the Euclidean space IR^n and the basic notions and results concerning the single valued and multivariable differential and integral calculus.	

IV. Course contents
1.	Real number system. The algebraic and topological structure of the real axis.
2.	Sequences and series of real numbers. Limits and continuity on IR.  
3.	Diferential calculus on the real axis: definitions, properties, mean value theorems, higher order derivatives, Taylor formula, study of functions variations, problemes on the existence of extremum points, primitives.
4.	Integral calculus on the real axis.
5.	Euclidean spaceSpatiul IR^n: its algebraic and topological  structure.
6.	Limits and continuity of vector valued functions of vector variables.  
7.	Derivatives, partial derivatives, and differentials of vector valued functions of vector variables. Higher order derivatives, partial derivatives, and differentials. Taylor formula.
8.	Inverse function theorem. Implicit functions.  
9.	Existence of local extremum point. Constrained problems. Lagrange multipliers rule. 
10.	Duble and triple integrals. Improper integrals.
11.	Sequences and series of functions.
12.	Beta and gamma functions of Euler.

V. Bibliography
1. ANDRICA D., DUCA I.D., PURDEA I., POP I.: Matematica de baza, Studium, Cluj-Napoca, 2002. 
2. BALAZS M., KOLUMBAN I.: Analiza matematica,Curs litografiat, Facultatea de Matematica, Univ. $Babes-Bolyai$. 
3. BRECKNER W. W.: Analiza matematica. Topologia spatiului R^n Cluj-Napoca, Universitatea, 1985. 
4. COBZAS S.: Analiza matematica (Calcul diferential), Presa Universitara Clujeana, Cluj-Napoca, 1998. 
5. MARUSCIAC I.: Analiza matematica. I, II, Cluj-Napoca, Universitatea $Babes-Bolyai$, 1980. 
6. MEGAN M.: Bazele analizei matematice,  Ed. BIT, Timisoara, vol I - III, 2000, 2001, 2002.
7. MURESAN, M.: Mathematical Analysis and Appications, Risoprint, Cluj-Napoca, 
8. MURESAN, M.:  A Concret Approach to Classical Analysis, Springer, New York, 2008.
9. FIHTENHOLT G. M.: Curs de calcul diferential si integral, Vol. I, II. Bucuresti, Editura Tehnica, 1965. 
9. TRIF T.: Probleme de calcul diferential si integral in IR^n, Casa Cartii de Stiinta, Cluj-Napoca, 2003. 

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Written and oral exam.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Prof. MURESAN Marian, Ph.D.