"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Mathematical analysis (2)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO021
2
2+2+0
6
compulsory
Informatică
Teaching Staff in Charge
Assoc.Prof. LUPSA Liana, Ph.D., llupsa@math.ubbcluj.ro
Assoc.Prof. GOLDNER Gavril, Ph.D., goldner@math.ubbcluj.ro
Aims
Presentation of the main notions and results about integrability of functions and about sequences and series of functions.
Content
The basic notions and results concerning the multivariable differential and integral calculus are presented. The main topics included are: differentiability of vector functions of vector variable, mean value theorems for differentiable functions, partial derivatives, optimality conditions, the inverse function theorem, differentiable implicit functions, optimization problems having equations as constraints, the Riemann integral of a real-valued function defined on an interval in R^n, the Riemann integral of a real-valued function defined on a bounded set in R^n, iterated integrals, Jordan measurable sets, Lebesgue's criterion of Riemann integrability, change of variables in the multiple Riemann integral.
References
1. BALAZS M., KOLUMBAN I.: Analiza matematica. Curs litografiat, Facultatea de Matematica, Univ. "Babes-Bolyai".
2. COBZAS ST.: Analiza matematica (Calcul diferential). Cluj-Napoca, Presa Universitara Clujeana, 1998.
3. COLOJOARA I.: Analiza matematica. Editura Didactica si Pedagogica, Bucuresti, 1983.
4. LUPSA L. si BLAGA L.: Elemente de analiza matematica si teoria campului. Partea II. Cluj-Napoca, Editura RISOPRINT, 2002.
5. MARUSCIAC I.: Analiza matematica. II. Cluj-Napoca, Universitatea "Babes-Bolyai", 1980.
6. FIHTENHOLT G. M.: Curs de calcul diferential si integral. Vol. II, III. Bucuresti, Editura Tehnica, 1965.
5. NICOLESCU M., DINCULEANU N., MARCUS S.: Manual de analiza matematica. Vol I, II. Bucuresti, Editura Didactica si Pedag., 1963.
Assessment
Written and oral exam.