subject

Differential equations

lecturers

Dr. Faragó István, professor

credits

2+2=4

period

5

curriculum

Fourier series. Basic notions of ordinary differential equations. Simple types of ordinary differential equations. Exact differential equations.  

Separable differential equations. First-order differential equations. Cauchy problem. Lipshitz property. Existence and uniqueness theorem. Linear first-order systems of differential equations, higher-order differential equations. Constant coefficient linear systems. The Sturm-Liouville problem. Basic stability notions. Basic notions of partial differential equations. Laplace equation. Heat equation (Poisson formula). Hyperbolic problems (D’Alembert formula).

Inhomogeneous problems on an infinite domain (Duhamel principle)

literature

Ponomarjov, K.K.   Differenciálegyenletek felállítása és megoldása, Tankönyvkiadó, 1969.

Tóth, J, Simon, P. Differenciálegyenletek. Typotex, 2005.

Simon, L. Baderko, E. A. Másodrendű lineáris parciális differenciálegyenletek, Tankönyvkiadó,
Budapest, 1983.

form of tuition

lectures, practical exercises

mode of assessment

Written exam, reporting