One should also be aware that probabilistic

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Unformatted text preview: de a better description of the phenomenon under study than a continuous one. One should also be aware that probabilistic techniques provide an additional component to model building, alongside the partial differential equations and discrete mechanical systems with many degrees of freedom described in these pages. There is a major dichotomy that runs through the subject—linear versus nonlinear. It is actually linear partial differential equations for which the technique of linear algebra prove to be so effective. This book is concerned primarly with linear partial differential equations—yet it is the nonlinear partial differential equations that provide the most intriguing questions for research. Nonlinear partial differential equations include the Einstein field equations from general relativity and the Navier-Stokes equations which describe fluid motion. We hope the linear theory presented here will whet the student’s appetite for studying the deeper waters of the nonlinear theory. The author would appreciate comments that may help improve the n...
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This document was uploaded on 01/12/2014.

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