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  3. Cambridge Texts in Applied Mathematics

The aim of this series is to provide a focus for publishing textbooks in applied mathematics at the advanced undergraduate and beginning graduate level. It is planned that the books will be devoted to covering certain mathematical techniques and theories and exploring their applications. The main audience for the series will be in departments of applied mathematics, engineering science or physics. It is important to recognize that for students, clear and careful exposition and a sound pedagogic presentation are frequently more relevant than surveying and synthesising recent developments. Authors will be encouraged to supply plenty of worked examples and exercises, of varying degrees of difficulty, for the reader. Books in the series should provide a solid understanding of how a given method can usefully be applied to help solve problems in physics and engineering.

  • Editorial Boards: M. J. Ablowitz, University of Colorado, Boulder, S. H. Davis, Northwestern University, Illinois , E. J. Hinch, University of Cambridge, A. Iserles, University of Cambridge, J. Ockendon, University of Oxford, P. J. Olver, University of Minnesota

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50 results in Cambridge Texts in Applied Mathematics

Page 3 of 3

Bäcklund and Darboux Transformations
  • Geometry and Modern Applications in Soliton Theory
  • C. Rogers, W. K. Schief
  • Published online:
    04 March 2010
    Print publication:
    24 June 2002
  • This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

An Introduction to Magnetohydrodynamics
  • P. A. Davidson
  • Published online:
    26 February 2010
    Print publication:
    05 March 2001
  • 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 magnetic field, which generates sunspots and solar flares, and the galactic field which influences the formation of stars. This is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids. This book is intended to serve as an introductory text for advanced undergraduates and postgraduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted towards incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text also contain an outline of the latest advances in the metallurgical applications of MHD and so are relevant to professional researchers in applied mathematics, engineering and metallurgy.

Boundary Integral and Singularity Methods for Linearized Viscous Flow
  • C. Pozrikidis
  • Published online:
    13 February 2010
    Print publication:
    28 February 1992
  • 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 text is supplemented with a number of examples and unsolved problems, many drawn from the field of particulate creeping flows. The material is selected so that the book may serve both as a reference monograph and as a textbook in a graduate course on fluid mechanics or computational fluid mechanics.

Vorticity and Incompressible Flow
  • Andrew J. Majda, Andrea L. Bertozzi
  • Published online:
    03 February 2010
    Print publication:
    26 November 2001
  • 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 book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. 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.

Applied Solid Mechanics
  • Peter Howell, Gregory Kozyreff, John Ockendon
  • Published online:
    02 February 2010
    Print publication:
    11 December 2008
  • 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 biomechanics. The variety of materials (metals, rocks, glasses, sand, flesh and bone) and their properties (porosity, viscosity, elasticity, plasticity) is reflected by the concepts and techniques needed to understand them: a rich mixture of mathematics, physics and experiment. These are all combined in this unique book, based on years of experience in research and teaching. Starting from the simplest situations, models of increasing sophistication are derived and applied. The emphasis is on problem-solving and building intuition, rather than a technical presentation of theory. The text is complemented by over 100 carefully-chosen exercises, making this an ideal companion for students taking advanced courses, or those undertaking research in this or related disciplines.

Applied Analysis of the Navier-Stokes Equations
  • Charles R. Doering, J. D. Gibbon
  • Published online:
    02 February 2010
    Print publication:
    28 April 1995
  • 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 atmospheric science. This book is an introductory physical and mathematical presentation of the Navier–Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. Intended for graduate students and researchers in applied mathematics and theoretical physics, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses.

A First Course in Combinatorial Optimization
  • Jon Lee
  • Published online:
    28 January 2010
    Print publication:
    09 February 2004
  • 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 mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.

Symmetry Methods for Differential Equations
  • A Beginner's Guide
  • Peter E. Hydon
  • Published online:
    13 January 2010
    Print publication:
    28 January 2000
  • 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 differential equations of an unfamiliar type; they do not rely on special 'tricks'. Instead, a given differential equation is forced to reveal its symmetries, which are then used to construct exact solutions. This book is a straightforward introduction to the subject, 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 written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily. The book contains methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.

An Introduction to Parallel and Vector Scientific Computation
  • Ronald W. Shonkwiler, Lew Lefton
  • Published online:
    12 December 2009
    Print publication:
    14 August 2006
  • 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 general examination of timing, data dependencies, and communication. These ideas are implemented with respect to shared memory, parallel and vector processing, and distributed memory cluster computing. Threads, OpenMP, and MPI are covered, along with code examples in Fortran, C, and Java. The principles of parallel computation are applied throughout as the authors cover traditional topics in a first course in scientific computing. Building on the fundamentals of floating point representation and numerical error, a thorough treatment of numerical linear algebra and eigenvector/eigenvalue problems is provided. By studying how these algorithms parallelize, the reader is able to explore parallelism inherent in other computations, such as Monte Carlo methods.

Maximum and Minimum Principles
  • A Unified Approach with Applications
  • M. J. Sewell
  • Published online:
    12 October 2009
    Print publication:
    17 December 1987
  • 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. There are several features, including a chapter on the Legendre dual transformation and some of its singularities. Many substantial examples and exercises are included, especially from the mechanics of fluids, elastic and plastic solids and from optimisation theory. The saddle functional viewpoint gives the book a wide scope. The treatment is straightforward, the only prerequisite being a basic knowledge of the calculus of variations. Part of the book is based on final-year undergraduate courses. This is developed into an account which will interest a wide range of students and professionals in applied mathematics, engineering, physics and operations research.

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