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

Code	Subject	
MMA0002	Mathematical Analysis	

Section	Semester	Hours: C+S+L	Category	Type	
Computer Science	1	3+2+0	fundamental	compulsory	
Information engineering	1	3+2+0		compulsory	

Teaching Staff in Charge	Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro
Assoc.Prof. TRIF Tiberiu Vasile, Ph.D., ttrif@math.ubbcluj.ro
Prof. KASSAY Gabor, Ph.D., kassay@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. 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.
	
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. 
	
Assessment	Written and oral exam.