MAT 306 Theory of Functions of a Complex Variable

Complex Numbers,polar and exponential forms of comlex numbers,Functions of a complex variable,Limit,continuity and Derivatives,Analytic Functions,Elementary Functıons,Integrals,Line Integrals,Series,Residues and poles,Mapping by elementary Functions,Conformal Mapping and its applications.

MAT 344 Partial Differential Equations

First order equations; linear and quasilinear equations. Methods of characteristics (Lagrange’s method), characteristic curves. Cauchy problem for linear and quasiliner equations. Existence and uniqueness theorem. Classification of second order linear partial  differential equations; canonical forms. Cauchy  problem in two independent variables. Cauchy-Kowalewski theorem. The Cauchy problem for the wave equation. Dirichlet and Neumann problems for the Laplace equation, maximum principle. Heat equation on the strip. Method of eifenfunction expansio using Green’s function.