Waves and Compressible Flow

ISBN-13: 9781441923356 / Angielski / Miękka / 2010 / 190 str.

Hilary Ockendon; John R. Ockendon

Opis

Mathematics is playing an ever more important role in the physical and biol- ical sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and tea- ing, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Contents The starred sections are self-contained and may be omitted at a ?rst reading.

Recenzje

From the reviews:

"The volume by Ockendon and Ockendon ... updates the 1983 Inviscid Fluid Flows, by H. Ockendon and Alan B. Tayler. In this new book they view gas dynamics as a paradigm for more general wave propagation. Chapter 2 ... will particularly benefit undergraduate readers. ... Throughout, the authors develop serious applications both in the text and in the exercises. Overall, this is a very inviting introduction to a notoriously difficult subject. ... Highly recommended." (D.V. Feldman, CHOICE, Vol. 42 (5), January, 2005)

"This book, a welcome addition to the literature on the application of linear ... . in its present completely rewritten and updated form, it reflects the widening of interest that has subsequently taken place in the study of nonlinear waves in the physical sciences. ... The range of topics covered will be both a benefit to students and a stimulus ... . This is a good book that will be appreciated by all students who wish to gain a sound understanding ... ." (Alan Jeffrey, Zentralblatt MATH, Vol. 1041 (16), 2004)

"This book ... is an introduction to the theory of linear and nonlinear waves in fluids, including the theory of shock waves. ... is extraordinarily accurate and free of misprints ... . I enjoyed reading this book. ... most attractive and enticing appearance, and I'm certain that many readers who browse through it will wish to buy a copy. The exercises ... are excellent. ... A beginner who worked through these exercises would not only enjoy himself or herself ... ." (C. J. Chapman, Journal of Fluid Mechanics, Vol. 521, 2004)

"The book targets a readership of final year undergraduates and first year graduates in applied mathematics. In the reviewer's opinion, it is very well designed to catch the student's interest ... while every chapter displays essential features in some important area of fluid dynamics. Additionally, students may practice by solving 91 exercises. This volume is mainly devoted to inviscid flows. ... The book is very well written." (Denis Serre, Mathematical Reviews, 2004)

Spis treści

Series Preface.-Introduction.- The equations of Inviscid Compressible Flow.- Models for Linear Wave Propagation.- Theories for Linear Waves.- Nonlinear Waves in Fluids.-Shock waves.- Epilogue.- References.- Index

Blurb

 

This book aims to give readers a broad mathematical basis for modeling and understanding the wide range of wave phenomena encountered in modern applications, especially in gasdynamics. The material originated from a coarse that has been taught at Oxford University for many years. It is a development of  Inviscid Fluid Flows, by H. Ockendon and A. B. Tayler (Springer, 1983), which has been retitled and completely rewritten to reflect current research interests. In particular, a more comprehensive collection of models is used to illustrate the underpinning mathematical methodologies. These methodologies have been expanded to include the basic ideas of hyperbolic differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how wave phenomena in other areas such as electromagnetism and solid mechanics can be treated using similar techniques.

Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, engineering, and other physical sciences.