Subject: Partial Differential Equations (1)	Code: ME003	

Semester	 Hours: C+S+L	Type	 Section	
5	2+2+0	compulsory	Mathematics	
7	2+2+0	compulsory	Mathematics-Computer Science	
7	2+2+0	compulsory	Applied Mathematics	

Teaching Staff in Charge	Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro
Prof. TRIF Damian, Ph.D., dtrif@math.ubbcluj.ro
Assoc.Prof. BEGE Antal, Ph.D., bege@math.ubbcluj.ro	
Aims	Assimilation of the basic elements of classical and modern theory of 
linear partial differential equations	
Content	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	
Selective References	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. PRECUP, R., Lectii de ecuatii cu derivate partiale, Presa Universitara Clujeana, 2004.
5. SIMON, L., BADERKO, E.A., Másodrendu parciális differenciálegyenletek, Tankönyvkiadó, Budapest, 1983.
6. SZILÁGYI P., Másodrendu parciális differenciálegyenletek, BBTE, Kolozsvár, 1998.
7. VLADIMIROV, V.S., Ecuatiile fizicii matematice, Ed. St. Enc., Bucuresti, 1981 (Bevezetés a parciális differenciálegyenletek elméletébe, Muszaki Kiadó, Budapest, 1980).
8. TRIF, D., Ecuatii cu derivate partiale, UBB, Cluj, 1993.	
Assessment	Written and oral examinatio