MMA0002 | Mathematical Analysis |
Teaching Staff in Charge |
Prof. MURESAN Marian, Ph.D., mmarianmath.ubbcluj.ro Prof. KASSAY Gabor, Ph.D., kassaymath.ubbcluj.ro Lect. BERINDE Stefan Gheorghe, Ph.D., sberindemath.ubbcluj.ro Assoc.Prof. DIACONU Adrian, Ph.D., adiaconumath.ubbcluj.ro Assoc.Prof. SÁNDOR Jozsef, Ph.D., jsandormath.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.
2 Sequences of real numbers. The algebraic and topological structure of the real axis. 3. Completeness of the real axis. Series of real numbers. 4. Real functions of a real variable. Limits, continuity, monotonic functions, Lipschitz functions, Banach fixed point theorem, and convex functions. 5. Diferential calculus on the real axis: definitions, properties, mean value theorems, higher order derivatives, Taylor formula, and the study of functions variations. 6. Problemes on the existence of extremum points. 7. Primitives. Defined integrals, the Leibnitz-Newton formula. 8. The Darboux-Stieltjes formula. 9. Vector functions of vector argument. 10. Continuity, the Frechet differential. 11. Partial derivatives. 12. Second and higher order Frechet differential. 13. Existence of local extremum points. Inverse function theorem. Implicit functions. 14. Duble and triple integrals. |
References |
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 Concrete Approach to Classical Analysis, Springer, New York, 2009. 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. |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |