ABSTRACT
This chapter shows how seemingly different physical processes can be modeled by differential equations that have the same functional forms. It attempts to derive each equation with a different method. All differential equations derived are second order in space coordinates and first order in time domain. Solving a differential equation implies that we begin from the given initial and boundary conditions and use the differential equation to extrapolate our desired variable to the space and time of interest. When the material properties are functions of the dependent variable, the differential equations become nonlinear and usually require iterative numerical solutions. How to match boundary conditions and cope with variations in material properties dictates how a differential equation or a boundary-value problem is solved.
