This preview shows page 1. Sign up to view the full content.
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...
View Full Document
This document was uploaded on 01/12/2014.
- Winter '14