**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.*

—

*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.*

—

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