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

Mathematical analysis (1)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO001
1
2+2+0
6
compulsory
Matematică
MO001
1
2+2+0
6
compulsory
Informatică
MO001
1
2+2+0
6
compulsory
Matematică-Informatică
MO001
1
2+2+0
6
compulsory
Matematici Aplicate
Teaching Staff in Charge
Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro
Prof. DUCA Dorel, Ph.D., dduca@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 topology of the real axis and the differential and integral calculus of functions of one real variable.
Content
I. The Euclidean space R^n. Elements of topology in R^n; the completeness of R^n.
Compact sets.
II. Real and vectorial functions of one or several real variables. The limit of a
vectorial function of several real variables at a point. Continuous vectorial
function of several real variables at a point. Properties of continuous
functions defined on a compact set. Linear functions.
III. First order derivability and differentiability. Directional derivative;
partial derivatives. First order Frechet differentiability. Properties of
differentiable functions at a point.
IV. Second order and higher order derivability and differentiability. Second order
and higher order partial derivatives. Schwarz theorem. Second and higher order
Frechet differentiability. Young theorem. Taylor formula.
V. Implicit functions. The notion of implicit function. Implicit function theorem.
VI. Applications of differential calculus for finding local extremum points.
The definition of a local extremum point; Fermat theorem for functions of vector
variables; sufficient conditions of a local extremum. Conditional extremum.
VII. Numerical series. Sequences of functions.
References
l. Balazs M.: Matematikai analizis, Cluj-Napoca, Egyetemi Tankonyvtanacs, 2000.
2. Balazs M., Kolumban I.: Matematikai analizis, Dacia Konyvkiado, Cluj-Napoca, 1978
3. Breckner W.W.: Analiza matematica. Topologia spatiului Rn, Cluj-Napoca, Universitatea, 1985
4. Bucur G., Campu E., Gaina S.: Culegere de probleme de calcul diferential si integral, II, Editura tehnica, Bucuresti, 1966
5. Cobzas St.: Analiza matematica (Calcul diferential), Presa Universitara Clujeana, Cluj-Napoca, 1997
6. Duca D.I., Duca E.: Culegere de probleme de analiza matematica, 1, 2, Editura GIL, Zalau, 1996, 1997
7. Luenburg H.: Vorlesungen uber Analysis, Manheim, Bibliographisches Institut, 1981
8. Marusciac I.: Analiza matematica, I, Universitatea Babes-Bolyai, Cluj-Napoca, 1980
9. Siretchi Gh.: Calcul diferential si integral, I, II, Editura Stiintifica si Enciclopedica, Bucuresti, 1985
10. ***: Analiza matematica, I, Ed. a V-a, Editura Didactica si Pedagogica, Bucuresti, 1980
Assessment
Exam.