Mathematical analysis (1) |
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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. |