"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
MO002
2
2+2+0
6
compulsory
Matematică
MO002
2
2+2+0
6
compulsory
Informatică
MO002
2
2+2+0
5
compulsory
Matematică-Informatică
MO002
2
2+2+0
6
compulsory
Matematici Aplicate
Teaching Staff in Charge
Lect. TRIF Tiberiu Vasile, Ph.D., ttrif@math.ubbcluj.ro
Prof. BRECKNER Wolfgang, Ph.D., breckner@math.ubbcluj.ro
Assoc.Prof. LUPSA Liana, Ph.D., llupsa@math.ubbcluj.ro
Assoc.Prof. SÁNDOR Jozsef, Ph.D., jsandor@math.ubbcluj.ro
Aims
Getting to know the differential and integral calculus of the real functions of several real variables.
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
l. Balázs M.: Matematikai analizis, Erdélyi Tankönyvtanács, Kolozsvár, 2000
2. Balázs M., Kolumbán I.: Matematikai analizis, Dacia Könyvkiadό, Kolozsvár-Napoca, 1978
3. Browder A.: Mathematical Analysis. An Introduction, Springer-Verlag, New York, 1996
4. Bucur G., Câmpu E., Găină S.: Culegere de probleme de calcul diferenţial şi integral, III, Editura Tehnică, Bucureşti, 1967
5. Cobzaş Şt.: Analiză matematică (Calcul diferenţial), Presa Universitară Clujeană, Cluj-Napoca, 1997
6. Demidovici B.P.: Culegere de probleme şi exerciţii de analiză matematică, Editura Tehnică, Bucureşti, 1956
7. Heuser H.: Lehrbuch der Analysis, Teil 1, 11. Auflage, B. G. Teubner, Stuttgart, 1994;
Teil 2, 9. Auflage, B. G. Teubner, Stuttgart, 1995
8. Megan M.: Calcul diferenţial şi integral în R^p, Universitatea de Vest, Timişoara, 2000
9. Rudin W.: Principles of Mathematical Analysis, 2nd Edition, McGraw-Hill, New York, 1964
10. Walter W.: Analysis, I, II, Springer-Verlag, Berlin, 1990
Assessment
Exam.