MMA0002 | Mathematical Analysis |
Teaching Staff in Charge |
Prof. MURESAN Marian, Ph.D., mmarianmath.ubbcluj.ro Assoc.Prof. TRIF Tiberiu Vasile, Ph.D., ttrifmath.ubbcluj.ro Prof. KASSAY Gabor, Ph.D., kassaymath.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. The algebraic and topological structure of the real axis.
2. Sequences and series of real numbers. Limits and continuity on IR. 3. Diferential calculus on the real axis: definitions, properties, mean value theorems, higher order derivatives, Taylor formula, study of functions variations, problemes on the existence of extremum points, primitives. 4. Integral calculus on the real axis. 5. Euclidean spaceSpatiul IR^n: its algebraic and topological structure. 6. Limits and continuity of vector valued functions of vector variables. 7. Derivatives, partial derivatives, and differentials of vector valued functions of vector variables. Higher order derivatives, partial derivatives, and differentials. Taylor formula. 8. Inverse function theorem. Implicit functions. 9. Existence of local extremum point. Constrained problems. Lagrange multipliers rule. 10. Duble and triple integrals. Improper integrals. 11. Sequences and series of functions. 12. Beta and gamma functions of Euler. |
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 Concret Approach to Classical Analysis, Springer, New York, 2008. 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 |