Bücher der Reihe Cambridge Texts in Applied Mathematics

This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint.

This practical introduction covers mathematical methods for the analysis of stochastic models and their biological applications. Based on courses taught at the University of Oxford, the book can be used for self-study or as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics.

This book offers a rigorous introduction to geometric and topological inference, a rapidly evolving field that intersects computational geometry, applied topology, and data analysis. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. This book will be of particular use to applied mathematicians, engineers, computer scientists, and to all those interested in efficiently solving linear problems.

This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.

An outstanding resource for every teacher and student of the mechanics of continuous media. The author's unique approach, using the concept of intermediate asymptotics, has been tried and tested over a period of forty years teaching the subject in Russia, Europe and America.

This book serves as a concise introductory text on stochastic dynamics for applied mathematicians. Rich with examples, illustrations, and exercises with their solutions, it provides an accessible introduction to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty, from analytical, deterministic, structural and numerical perspectives.

This book describes the underlying approximation techniques and methods for finding solutions to nonlinear wave equations. Many chapters include exercise sets. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows.

In this introductory text, the fundamental algorithms of numerical linear algebra are developed in a parallel context. Topics include direct and iterative methods for solving linear systems, numerical methods for the eigenvector/eigenvalue problem and applications to Monte Carlo methods.

In many problems of applied mathematics, science, engineering or economics, an energy expenditure or its analogue can be approximated by upper and lower bounds. This book provides a unified account of the theory required to establish such bounds, by expressing the governing conditions of the problem, and the bounds, in terms of a saddle functional and its gradients.

Wave propagation and scattering are often very complex processes. One way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers.

This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. This is ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

This book presents a coherent introduction to boundary integral, boundary element and singularity methods for steady and unsteady flow at zero Reynolds number. The focus of the discussion is not only on the theoretical foundation, but also on the practical application and computer implementation.

The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems.

The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics.

This book follows the macroscopic, phenomenological approach which proposes equations abstracted from generally accepted experimental facts, studies the adequacy of the consequences drawn from these equations to those facts and then provides useful tools for designers and engineers.

This introduction to the mathematics of waves is for undergraduates in mathematics, physics or engineering. Further material on linear and nonlinear waves is also included for the benefit of graduates. The context and underlying physics is clearly explained; worked examples and exercises are supplied throughout, with solutions available to teachers.

This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

While mastery of ordinary differential equations is essential for students in many disciplines, adhering to any one method of solving them is not: this book stresses alternative examples and analyses ways the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour.

High-Speed Flow is a textbook suitable for undergraduates, postgraduates, and research workers in fluid dynamics. It covers such topics as subsonic and supersonic flight, shock waves and high-speed aerofoils. The book contains exercises and an extensive bibliography, providing access to the entire literature from 1860 to the present day.

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes many traditional elements of the subject. It gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems.

This book is a straightforward introduction to symmetry methods, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is designed to enable postgraduates and advanced undergraduates to master the main techniques quickly and easily.

Instability of flows and their transition to turbulence are widespread phenomena in engineering and nature, and are also important in many applied sciences. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments.

This 2003 book describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity. It demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be applied, and when they cannot.

This book explores the profound connections between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces. Punctuated with exercises, it is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.

The aim of this book is to present the concepts, methods and applications of kinetic theory to rarefied gas dynamics. Each section is accompanied by problems which are intended to demonstrate the use of the material in the text. For graduate courses in aerospace engineering or applied mathematics.

Used either by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them. Topics include distributions, asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow.

The book is an introduction to theory of sound generation by fluid flow, specially written for a one semester course at advanced undergraduate or graduate level. Problems are provided at the end of each chapter, many of which can be used for extended student projects. A whole chapter is devoted to worked examples.

The theory of water waves has been a source of intriguing mathematical problems for at least 150 years. This text considers the classical problems in linear and non-linear water-wave theory, as well as more modern aspects - problems that give rise to soliton-type equations. Lastly it examines the effects of viscosity.