**Graduate Studies in Mathematics**

Volume: 109;
2010;
265 pp;
Hardcover

MSC: Primary 35; 44; 76;

Print ISBN: 978-0-8218-4083-2

Product Code: GSM/109

List Price: $62.00

Individual Member Price: $49.60

**Electronic ISBN: 978-1-4704-1172-5
Product Code: GSM/109.E**

List Price: $62.00

Individual Member Price: $49.60

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#### Supplemental Materials

# Training Manual on Transport and Fluids

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*John C. Neu*

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.

#### Table of Contents

# Table of Contents

## Training Manual on Transport and Fluids

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface xi12 free
- Part I. Transport processes: the basic prototypes 114 free
- Convection 316
- Diffusion 3144
- Local conservation laws 6174
- Part II. Superposition 8598
- Superposition of point source solutions 87100
- 𝛿-functions 115128
- Part III. Scaling-based reductions in basic fluid mechanics 141154
- Ideal fluid mechanics 143156
- Free surface waves 187200
- Solution of the shallow water equations 209222
- Bibliography 257270
- Index 259272 free
- Back Cover Back Cover1282

#### Readership

Graduate students and research mathematicians interested in applications of PDE to physics, in particular, fluid dynamics.

#### Reviews

[T]he book tells stories in a very dynamic fashion, based on many problems with solutions, most of them having an important applicative content.

-- Thierry Goudon, Mathematical Reviews