Subject: Partial Differential Equations (2)	Code: ME004	

Semester	 Hours: C+S+L	Type	 Section	
6	2+1+0	compulsory	Mathematics	
8	2+2+0	optional	Applied Mathematics	

Teaching Staff in Charge	Prof. TRIF Damian, Ph.D., dtrif@math.ubbcluj.ro
Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro
Assoc.Prof. BEGE Antal, Ph.D., bege@math.ubbcluj.ro	
Aims	Improvement of the working methods in Sobolev spaces in view of 
the study of nonlinear boundary value problems	
Content	Distributions; Sobolev spaces; Fourier transform;First order partial differential equations; Generalized solutions 
to elliptic problems; Regularity results. Maximum principles. 
Eigenvalues and eigenfunctions. Introduction to potential theory	
Selective References	1. ADAMS, R.A., Sobolev spaces, Academic Press, 1975.
2. BARBU, V., Probleme la limita pentru ecuatii cu derivate partiale, Ed. Acad. Române, Bucuresti, 1993.
3. DEBNAT, L., Non-linear partial differential equations for scientists and engineers, Birkhauser, Berlin, 1997.
4. GILBARG, D., TRUDINGER, N.S., Elliptic partial differential equations of second order, Springer, Berlin, 1983.
5. O'REGAN, D., PRECUP, R., Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001. 
6. PRECUP, R., Lectii de ecuatii cu derivate partiale, Presa Universitara Clujeana, 2004.
7. RAUCH, J., Partial differential equations, Springer, Berlin, 1991.
8. SZILAGYI 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	Midterm exam 30%
Final written exam 70%