Cambridge Texts in Applied Mathematics – serie
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97 produkter
97 produkter
Del 35 - Cambridge Texts in Applied Mathematics
Complex Variables
Introduction and Applications
Häftad, Engelska, 2003
992 kr
Skickas inom 7-10 vardagar
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.
Del 31 - Cambridge Texts in Applied Mathematics
Finite Volume Methods for Hyperbolic Problems
Häftad, Engelska, 2002
966 kr
Skickas inom 7-10 vardagar
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. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Del 32 - Cambridge Texts in Applied Mathematics
Introduction to Hydrodynamic Stability
Häftad, Engelska, 2002
702 kr
Skickas inom 7-10 vardagar
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 as engineering. 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. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Del 36 - Cambridge Texts in Applied Mathematics
A First Course in Combinatorial Optimization
Häftad, Engelska, 2004
603 kr
Skickas inom 7-10 vardagar
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.
Del 33 - Cambridge Texts in Applied Mathematics
Theory of Vortex Sound
Häftad, Engelska, 2002
500 kr
Skickas inom 7-10 vardagar
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 explain underlying fluid mechanical and acoustic concepts, and to describe as fully as possible the steps in a complicated derivation. The discussion deals specifically with low Mach number flows, which enables the sound produced by 'vortex-surface' interactions to be analysed using the 'compact Green's function'. This provides a routine procedure for estimating the sound, and an easy identification of those parts of a structure that are likely to be important sources of sound. Each chapter ends with a set of problems, many of which can form the basis of an extended student project. The final chapter contains worked examples that have been investigated by students at Boston University.
Del 30 - Cambridge Texts in Applied Mathematics
Bäcklund and Darboux Transformations
Geometry and Modern Applications in Soliton Theory
Häftad, Engelska, 2002
739 kr
Skickas inom 7-10 vardagar
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.
Del 37 - Cambridge Texts in Applied Mathematics
Hydrodynamic Instabilities
Häftad, Engelska, 2011
987 kr
Skickas inom 7-10 vardagar
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 student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.
Del 45 - Cambridge Texts in Applied Mathematics
A Physical Introduction to Suspension Dynamics
Häftad, Engelska, 2011
553 kr
Skickas inom 7-10 vardagar
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 viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.
Del 46 - Cambridge Texts in Applied Mathematics
Iterative Methods in Combinatorial Optimization
Häftad, Engelska, 2011
615 kr
Skickas inom 7-10 vardagar
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 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. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.
Del 45 - Cambridge Texts in Applied Mathematics
A Physical Introduction to Suspension Dynamics
Inbunden, Engelska, 2011
1 512 kr
Skickas inom 7-10 vardagar
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 viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.
Del 2 - Cambridge Texts in Applied Mathematics
Solitons
An Introduction
Häftad, Engelska, 1989
634 kr
Skickas inom 7-10 vardagar
This textbook is an introduction to the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. The authors explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Transform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites (i.e., partial differential equations, calculus of variations, Fourier integrals, linear waves and Sturm-Liouville theory), and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas, and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to the solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.
Del 5 - Cambridge Texts in Applied Mathematics
Integral Equations: A Practical Treatment, from Spectral Theory to Applications
Häftad, Engelska, 1990
685 kr
Skickas inom 7-10 vardagar
This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems. The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text and it allows a thorough account to be given of many of the types of integral equation which arise in application areas. Since it is not always possible to find explicit solutions of the problems posed, much attention is devoted to obtaining qualitative information and approximations to the solutions, with the associated error estimates. This treatment is intended for final year mathematics undergraduates, postgraduates and research workers in application areas such as numerical analysis and fluid mechanics.
Del 1 - Cambridge Texts in Applied Mathematics
Maximum and Minimum Principles
A Unified Approach with Applications
Häftad, Engelska, 1987
838 kr
Skickas inom 7-10 vardagar
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.
Del 3 - Cambridge Texts in Applied Mathematics
The Kinematics of Mixing
Stretching, Chaos, and Transport
Häftad, Engelska, 1989
987 kr
Skickas inom 7-10 vardagar
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 author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included.
Del 6 - Cambridge Texts in Applied Mathematics
Perturbation Methods
Häftad, Engelska, 1991
583 kr
Skickas inom 7-10 vardagar
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 text wide appeal to students from a broad range of disciplines. Asymptotic expansions, strained coordinates and multiple scales are illustrated by copious use of examples drawn from all areas of applied mathematics and theoretical physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather to give a physical understanding of the subtle balances in a complex problem.
Del 9 - Cambridge Texts in Applied Mathematics
Nonlinear Wave Processes in Acoustics
Inbunden, Engelska, 1998
1 837 kr
Skickas inom 7-10 vardagar
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 of interest in nonlinear acoustic phenomena. The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. Consideration is given to the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction upon the evolution and interaction of acoustic beams. 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.
Del 7 - Cambridge Texts in Applied Mathematics
The Thermomechanics of Plasticity and Fracture
Inbunden, Engelska, 1992
1 490 kr
Skickas inom 7-10 vardagar
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 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. The material is drawn from the author's graduate course in Europe and the United States and may be used to form the basis for similar graduate courses on plasticity and fracture. Many worked examples are presented and each chapter concludes with problems for students. The book will thus undoubtedly establish itself as a core text for both students and researchers.
Del 7 - Cambridge Texts in Applied Mathematics
The Thermomechanics of Plasticity and Fracture
Häftad, Engelska, 1992
800 kr
Skickas inom 7-10 vardagar
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 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. The material is drawn from the author's graduate course in Europe and the United States and may be used to form the basis for similar graduate courses on plasticity and fracture. Many worked examples are presented and each chapter concludes with problems for students. The book will thus undoubtedly establish itself as a core text for both students and researchers.
Del 9 - Cambridge Texts in Applied Mathematics
Nonlinear Wave Processes in Acoustics
Häftad, Engelska, 1998
813 kr
Skickas inom 7-10 vardagar
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 of interest in nonlinear acoustic phenomena. The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. Consideration is given to the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction upon the evolution and interaction of acoustic beams. 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.
Del 8 - Cambridge Texts in Applied Mathematics
Boundary Integral and Singularity Methods for Linearized Viscous Flow
Inbunden, Engelska, 1992
2 161 kr
Skickas inom 7-10 vardagar
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.
Del 10 - Cambridge Texts in Applied Mathematics
Nonlinear Systems
Häftad, Engelska, 1992
838 kr
Skickas inom 7-10 vardagar
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 together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.
Del 8 - Cambridge Texts in Applied Mathematics
Boundary Integral and Singularity Methods for Linearized Viscous Flow
Häftad, Engelska, 1992
603 kr
Skickas inom 7-10 vardagar
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.
Del 11 - Cambridge Texts in Applied Mathematics
Stability, Instability and Chaos
An Introduction to the Theory of Nonlinear Differential Equations
Häftad, Engelska, 1994
950 kr
Skickas inom 7-10 vardagar
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 Poincaré-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.
Del 14 - Cambridge Texts in Applied Mathematics
Scaling, Self-similarity, and Intermediate Asymptotics
Dimensional Analysis and Intermediate Asymptotics
Häftad, Engelska, 1996
1 037 kr
Skickas inom 7-10 vardagar
Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. 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. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
Del 12 - Cambridge Texts in Applied Mathematics
Applied Analysis of the Navier-Stokes Equations
Häftad, Engelska, 1995
677 kr
Skickas inom 7-10 vardagar
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.
Del 13 - Cambridge Texts in Applied Mathematics
Viscous Flow
Inbunden, Engelska, 1995
621 kr
Skickas inom 7-10 vardagar
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 these phenomena are modelled is novel and suggestive of alternative methodologies. 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. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be 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.
Del 13 - Cambridge Texts in Applied Mathematics
Viscous Flow
Häftad, Engelska, 1995
378 kr
Skickas inom 7-10 vardagar
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 these phenomena are modelled is novel and suggestive of alternative methodologies. 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. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be 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.
Del 17 - Cambridge Texts in Applied Mathematics
Mathematical Models in the Applied Sciences
Häftad, Engelska, 1997
950 kr
Skickas inom 7-10 vardagar
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 in the techniques of modelling, and proceeds to explore a range of classical and continuum models from an impressive array of disciplines, including: biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. It assumes only a basic mathematical grounding in calculus and analysis and will provide a wealth of examples for students of mathematics, engineering, and the range of applied sciences.
Del 22 - Cambridge Texts in Applied Mathematics
Symmetry Methods for Differential Equations
A Beginner's Guide
Inbunden, Engelska, 2000
1 577 kr
Skickas inom 7-10 vardagar
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.
Del 22 - Cambridge Texts in Applied Mathematics
Symmetry Methods for Differential Equations
A Beginner's Guide
Häftad, Engelska, 2000
677 kr
Skickas inom 7-10 vardagar
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.