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Guide to Essential Math, 2nd Edition by Sy M. Blinder

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Chapter 13

Partial Differential Equations and Special Functions

13.1 Partial Differential Equations

Many complex physical, geometrical, and stochastic (probabilistic) phenomena are described by partial differential equations (PDEs), involving two or more independent variables. They are obviously much more difficult to solve than ordinary differential equations (ODEs). Some applications, including weather prediction, econometric models, fluid dynamics, and nuclear engineering, might involve simultaneous PDEs with large numbers of variables. Such problems are best tackled by powerful supercomputers. We will be content to consider a few representative second-order PDEs for which analytic solutions are possible.

Scalar and vector fields which depend ...

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