December 2019
Intermediate to advanced
960 pages
25h 46m
English
Content preview from Essentials of Mathematical Methods in Science and Engineering, 2nd Edition
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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)
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)
where 
is a physical constant depending on the characteristics of the environment. The wave equation
(14.3)
where 
stands for the wave velocity, is used to study wave phenomena in many different branches of science and engineering. Helmholtz equation
(14.4)
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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