"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Mathematical analysis (3) |
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| Teaching Staff in Charge |
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| Aims |
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Getting to know the classical knowledges of integral calculus of functions of one and several real variables. |
| Content |
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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 |
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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 |
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Exam. |