This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include first and second order partial differential equations, classification of second order linear partial differential equations, derivation of standard equation, methods of solution of initial and boundary value problems, separation of variables, Fourier series and their applications to boundary value problems in partial differential equation of engineering and physics, internal transform methods; Fourier and Laplace transforms and their application to boundary value problems.