CHAPTER 14PARTIAL DIFFERENTIAL EQUATIONS AND SEPARATION OF VARIABLES

Majority of the differential equations of physics and engineering are partial differential equations. Laplace equation

(14.1)equation

which plays a central role in potential theory, is encountered in electrostatics, magnetostatics, and stationary flow problems. Diffusion and flow or transfer problems are commonly described by the equation

(14.2)equation

where images is a physical constant depending on the characteristics of the environment. The wave equation

(14.3)equation

where images stands for the wave velocity, is used to study wave phenomena in many different branches of science and engineering. Helmholtz equation

(14.4)equation

is encountered in the study of waves and oscillations. Nonhomogeneous versions of these equations, where the right‐hand side is nonzero, are also frequently encountered. In general, the nonhomogeneous term represents sources, sinks, ...

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