Bücher der Reihe Cambridge Texts in 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.

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.

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 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.

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.

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.

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.

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.

Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.

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 book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium.

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 text is for a one-semester introductory graduate course for students of operations research, mathematics, and computer science covers linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. The author focuses on the key mathematical ideas that lead to useful models and algorithms.

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.

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

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.

By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincare-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.

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

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 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.

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.

A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

A wide range of mathematical tools and ideas are drawn together in the study of nonlinear equations, and the results applied to diverse and countless problems in all the natural and social sciences.

Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.