| Partial differential equations (1) |
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| Teaching Staff in Charge |
| Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro Prof. TRIF Damian, Ph.D., dtrif@math.ubbcluj.ro Prof. MICULA Gheorghe, Ph.D., ghmicula@math.ubbcluj.ro Assoc.Prof. BEGE Antal, Ph.D., bege@math.ubbcluj.ro Prof. SZILAGYI Paul, Ph.D., szilagyp@cs.ubbcluj.ro |
| Aims |
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Assimilation of the basic elements of classical and modern theory of
linear partial differential equations. |
| Content |
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1. Classical theory for partial differential equations of second order: fundamental solutions of Laplace equations, maximum principles, uniqueness theorems, Green functions.
2. Separable variables method. Fourier method. 3. Generalized solutions for Dirichlet and Neumann problems associated to Poisson and Laplace equations. 4. Fourier transform method in the theory of partial differential equations. |
| References |
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1. Barbu, V., Probleme la limita pentru ecuatii cu derivate partiale,
Ed. Acad. Române, Bucuresti, 1993. 2. Brézis, H., Analyse fonctionelle. Théorie et applications, Masson, Paris, 1983. 3. Gilbarg, D., Trudinger, N.S., Elliptic partial differential equations of second order, Springer, Berlin, 1983. 4. Kalik, C., Ecuatii cu derivate partiale, Ed. St. Enc., Bucuresti, 1980. 5. Mihlin, S.G., Ecuatii liniare cu derivate partiale, Ed. St. Enc., Bucuresti, 1983. 6. Precup, R., Ecuatii cu derivate partiale, Transilvania Press, Cluj, 1997. 7. Simon, L., Baderko, E.A., Másodrendu parciális differenciálegyenletek, Tankönyvkiadó, Budapest, 1983. 8. Szilágyi P., Másodrendu parciális differenciálegyenletek, BBTE, Kolozsvár, 1998. 9. Vladimirov, V.S., Ecuatiile fizicii matematice, Ed. St. Enc., Bucuresti, 1981 (Bevezetés a parciális differenciálegyenletek elméletébe, Muszaki Kiadó, Budapest, 1980). 10. Trif, D., Ecuatii cu derivate partiale, UBB, Cluj, 1993. |
| Assessment |
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Written and oral examination |