I have learned a lot from John Neu over the
past years, and his book reflects very well his sense of style and
purpose.
—Walter Craig, McMaster University,
Hamilton, Ontario, Canada and Fields Institute for Research in
Mathematical Sciences, Toronto, Ontario, Canada
John Neu's book presents the basic ideas of
fluid mechanics, and of the transport of matter, in a clear and
reader-friendly way. Then it proposes a collection of problems,
starting with easy ones and gradually leading up to harder ones. Each
problem is solved with all the steps explained. In the course of
solving these problems, many fundamental methods of analysis are
introduced and explained. This is an ideal book for use as a text, or
for individual study.
—Joseph B. Keller, Stanford
University
This book presents elementary models of transport in continuous media and
a corresponding body of mathematical technique. Physical topics include
convection and diffusion as the simplest models of transport; local
conservation laws with sources as the general framework of continuum
mechanics; ideal fluid as the simplest model of a medium with mass;
momentum and energy transport; and finally, free surface waves, in
particular, shallow water theory.
There is a strong emphasis on dimensional analysis and scaling. Some
topics, such as physical similarity and similarity solutions, are
traditional. In addition, there are reductions based on scaling, such as
incompressible flow as a limit of compressible flow, and shallow water
theory derived asymptotically from the full equations of free surface
waves. More and deeper examples are presented as problems, including a
series of problems that model a tsunami approaching the shore.
The problems form an embedded subtext to the book. Each problem is
followed by a detailed solution emphasizing process and craftsmanship.
The problems express the practice of applied mathematics as the
examination and re-examination of simple but essential ideas in many
interrelated examples.
Readership
Graduate students and research mathematicians interested in
applications of PDE to physics, in particular, fluid dynamics.