Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMA0002	Mathematical Analysis	

Semester	Hours: C+S+L+P	Category	Status	
1	2+2+0+0	fundamental	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.	Algebra, Mathematical Analysis and Geometry	*			

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. 
2  Sequences of real numbers. The algebraic and topological structure of the real axis.
3. Completeness of the real axis. Series of real numbers.
4. Real functions of a real variable. Limits, continuity, monotonic functions, Lipschitz functions, Banach fixed point theorem, and convex functions.
5. Diferential calculus on the real axis: definitions, properties, mean value theorems, higher order derivatives, Taylor formula, and the study of functions variations.
6. Problemes on the existence of extremum points.
7. Primitives. Defined integrals, the Leibnitz-Newton formula.
8. The Darboux-Stieltjes formula.
9. Vector functions of vector argument.
10. Continuity, the Frechet differential.
11. Partial derivatives.
12. Second and higher order Frechet differential.
13. Existence of local extremum points. Inverse function theorem. Implicit functions.  
14. Duble and triple integrals. 	

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 Concrete Approach to Classical Analysis, Springer, New York, 2009.
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.