The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave…
Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early c…
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 a…
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a cr…
Perturbation methods are one of the fundamental tools used by all applied mathematicians and theoretical physicists. In this book, the author has managed to present the theory and techniques underlying such methods in a manner which will give the te…
The theory of water waves has been a source of intriguing and often difficult mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of th…
This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint.
The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth o…
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 provid…
This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and pol…
A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some…
Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calcu…
The world around us, natural or man-made, is built and held together by solid materials. Understanding their behaviour is the task of solid mechanics, which is in turn applied to many areas, from earthquake mechanics to industry, construction to bio…
Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in…
This self-contained introduction to Numerical Linear Algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability…
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elem…
Mathematical modelling is the basis of almost all applied mathematics. A ‘real-world’ problem is dissected and phrased in a mathematical setting, allowing it to be simplified and ultimately solved. This book presents a thorough grounding…
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the b…
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic found…
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well a…
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 pr…
The book is an introduction to the branch of fluid mechanics concerned with the production of sound by hydrodynamic flows. It is designed for a one semester introductory course at advanced undergraduate or graduate level. Great care is taken to expl…
Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial…
Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when th…
The Navier–Stokes equations are a set of nonlinear partial differential equations comprising the fundamental dynamical description of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheri…
This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty qu…
The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn togethe…
Over forty years of teaching experience are distilled into this text. The guiding principle is the wide use of the concept of intermediate asymptotics, which enables the natural introduction of the modeling of real bodies by continua. Beginning with…
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to…
The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any s…
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modell…
This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigoro…
This book 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. These equations describe a wi…
In spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The a…
With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and…
This book concentrates upon the mathematical theory of plasticity and fracture as opposed to the physical theory of these fields, and is presented in the thermomechanical framework. It follows the macroscopic, phenomenological approach which propose…
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…
Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them…
Magnetic fields influence many natural and man-made flows. They are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field which is maintained by fluid motion in the earth's core, the solar…
The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector space…
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, high-speed aerofoils, and temperature changes. Starting from firs…
A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Wa…
Symmetry is the key to solving differential equations. There are many well-known techniques for obtaining exact solutions, but most of them are special cases of a few powerful symmetry methods. Furthermore, these methods can be applied to differenti…
The mathematical theory of stochastic dynamics has become an important tool in the modeling of uncertainty in many complex biological, physical, and chemical systems and in engineering applications - for example, gene regulation systems, neuronal ne…
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…
Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart…
In this text, students of applied mathematics, science and engineering are introduced to fundamental ways of thinking about the broad context of parallelism. The authors begin by giving the reader a deeper understanding of the issues through a gener…