Hilary Ockendon - Böcker

Applied Mathematics is the art of constructing mathematical models of observed phenomena so that both qualitative and quantitative results can be predicted by the use of analytical and numerical methods. Theoretical Mechanics is concerned with the study of those phenomena which can be ob­ served in everyday life in the physical world around us. It is often characterised by the macroscopic approach which allows the concept of an element or particle of material, small compared to the dimensions of the phenomena being modelled, yet large compared to the molecular size of the material. Then atomic and molecular phenomena appear only as quantities averaged over many molecules. It is therefore natural that the mathemati­ cal models derived are in terms of functions which are continuous and well behaved, and that the analytical and numerical methods required for their development are strongly dependent on the theory of partial and ordinary differential equations. Much pure research in Mathematics has been stimu­ lated by the need to develop models of real situations, and experimental observations have often led to important conjectures and theorems in Analysis. It is therefore important to present a careful account of both the physical or experimental observations and the mathematical analysis used. The authors believe that Fluid Mechanics offers a rich field for il­ lustrating the art of mathematical modelling, the power of mathematical analysis and the stimulus of applications to readily observed phenomena.

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.

Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications.  New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises.  Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial 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 intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includesa complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, engineering, and other physical sciences.  Reviews of the first edition:"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, but would rapidly acquire mastery of techniques used…in JFM and many other journals…" (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)