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

Mathematical analysis 3
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MMA0004
3
2+2+0
6
compulsory
Matematică
MMA0004
3
2+2+0
5
compulsory
Matematică informatică
MMA0004
3
2+2+0
6
compulsory
Matematici aplicate
Teaching Staff in Charge
Assoc.Prof. DIACONU Adrian, Ph.D.,  adiaconumath.ubbcluj.ro
Lect. FINTA Zoltan, Ph.D.,  fzoltanmath.ubbcluj.ro
Aims
Getting to know the classical knowledges of integral calculus of functions of one and several real variables.
Content
1. Supplement to the integral theory : the integrability and the integral of Darboux - Stieltjes and Riemann - Stieltjes. Conditions of integrability. Functions of bounded variation. Jordan's theorem. The connection with the Riemann - Stieltjes integrability.
2. Line integrals and surface integrals : paths in R^{n}. Rectifiable paths, length of a path. Line integrals of the first type and line integrals of the second type. The case of a total differential. Green's formula. Surface integral of the first type and surface
integrals of the second type. Formulas of Stokes and Gauss - Ostrogradski.
3. Integrals on manifolds : differential forms in R^{n}. The integrate of a differential form. The generalized formula of Stokes.
References
1. BALAZS M.: Analiza matematica, III si IV, Universitate, Cluj-Napoca, 1983,1984
2. BALAZS M., KOLUMBAN I.: Matematikai analizis, Dacia Konivkyado, Kolozsvar-Napoca, 1978
3. BOBOC N.: Analiza matematica, II, Universitate, Bucuresti, 1993
4. BUCUR G., CAMPU E., GAINA S.: Culegere de probleme de calcul diferential si integral, III, Editura tehnica, Bucuresti, 1967
5. COBZAS ST.: Analiza matematica (Calcul diferential), Presa universitara clujeana, Cluj-Napoca, 1997
6. COLOJOARA I.: Analiza matematica, Ed. did. si ped., Bucuresti, 1983
7. DEMIDOVICI B.P.: Culegere de probleme si exercitii de analiza matematica, Ed. tehnica, Bucuresti, 1956
8. SIKORSKI R.: Advanced Calculus, PWN-Polish Scientific Publishiers, Warsawa, 1969
9. WALTER W.: ANALYSIS I, Zweite Aufl. Berlin, Springer-Verlag,1990
10. ***: Analiza matematica, II, Ed. did. si pedag., Bucuresti, 1980
11. HEUSER H.: Lehrbuch der Analysis.Teil 2. 9. Auflage. Stuttgart: B. G. Teubner, 1995.
Assessment
Exam.