Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMA0002	Mathematical Analysis	

Section	Sem.	Hours: C+S+L	Category	Type	
Computer Science	1	2+2+0	fundamental	compulsory	
Information engineering	1	2+2+0	fundamental	compulsory	

Teaching Staff in Charge	Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro
Prof. KASSAY Gabor, Ph.D., kassay@math.ubbcluj.ro
Lect. BERINDE Stefan Gheorghe, Ph.D., sberinde@math.ubbcluj.ro
Assoc.Prof. DIACONU Adrian, Ph.D., adiaconu@math.ubbcluj.ro
Assoc.Prof. SÁNDOR Jozsef, Ph.D., jsandor@math.ubbcluj.ro	
Aims	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.	
Content	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. 	
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. 
	
Assessment	Written and oral exam.