ABSTRACT
This chapter introduces the linear partial differential equations (PDE) that are used for modelling physical phenomena with more than one independent variable. Frequently, the independent variables are time t and one or more of the spacial variables, which are usually denoted by x, y, and z. The chapter considers the initial boundary value problems for heat transfer equations when both the equation and the boundary conditions were homogeneous and problems when neither the equation nor the boundary conditions are homogeneous. A course on partial differential equations includes three types of equations: parabolic, hyperbolic, and elliptic equations. The formula led to a boom in options trading and legitimized scientifically the activities of the Chicago Board Options Exchange and other options markets around the world. The key financial insight behind the equation is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk."
