Hardcover ISBN:  9780821840832 
Product Code:  GSM/109 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 
Electronic ISBN:  9781470411725 
Product Code:  GSM/109.E 
List Price:  $62.00 
MAA Member Price:  $55.80 
AMS Member Price:  $49.60 

Book DetailsGraduate Studies in MathematicsVolume: 109; 2010; 265 ppMSC: Primary 35; 44; 76;
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 readerfriendly 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 reexamination of simple but essential ideas in many interrelated examples.ReadershipGraduate students and research mathematicians interested in applications of PDE to physics, in particular, fluid dynamics.

Table of Contents

Part 1. Transport processes: the basic prototypes

Chapter 1. Convection

Chapter 2. Diffusion

Chapter 3. Local conservation laws

Part 2. Superposition

Chapter 4. Superposition of point source solutions

Chapter 5. $\delta $functions

Part 3. Scalingbased reductions in basic fluid mechanics

Chapter 6. Ideal fluid mechanics

Chapter 7. Free surface waves

Chapter 8. Solution of the shallow water equations


Additional Material

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


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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 readerfriendly 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 reexamination of simple but essential ideas in many interrelated examples.
Graduate students and research mathematicians interested in applications of PDE to physics, in particular, fluid dynamics.

Part 1. Transport processes: the basic prototypes

Chapter 1. Convection

Chapter 2. Diffusion

Chapter 3. Local conservation laws

Part 2. Superposition

Chapter 4. Superposition of point source solutions

Chapter 5. $\delta $functions

Part 3. Scalingbased reductions in basic fluid mechanics

Chapter 6. Ideal fluid mechanics

Chapter 7. Free surface waves

Chapter 8. Solution of the shallow water equations

[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