Differential calculus and equations Books
Cambridge University Press Positive Harmonic Functions and Diffusion 45 Cambridge Studies in Advanced Mathematics Series Number 45
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£133.95
Cambridge University Press Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations
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£68.39
Cambridge University Press Chaotic Dynamics
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£38.94
Cambridge University Press Asymptotic Problems in Equatio
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£111.15
Cambridge University Press Design by Competition Making Design Competition Work Environment and Behavior
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£65.86
Cambridge University Press A Primer of Nonlinear Analysis 34 Cambridge Studies in Advanced Mathematics Series Number 34
Book SynopsisThis is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.Trade Review'There's no more economical or lucid introduction to the subject than this great little book.' The Mathematical IntelligencerTable of ContentsPreface; Preliminaries and notation; 1. Differential calculus; 2. Local inversion theorems; 3. Global inversion theorems; 4. Semilinear Dirichlet problems; 5. Bifurcation results; 6. Bifurcation problems; 7. Bifurcation of periodic solutions; Further reading.
£41.79
Cambridge University Press Dynamical Systems and Numerical Analysis
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£110.20
Cambridge University Press Symmetry Methods for Differential Equations
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£105.45
Cambridge University Press Symmetry Methods for Differential Equations A Beginners Guide 22 Cambridge Texts in Applied Mathematics Series Number 22
Book SynopsisSymmetry 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.Trade Review'Hydon's book stands out as perhaps the best introductory level text currently available … Hydon's book is extremely well-written, and a welcome addition to the literature on Lie's methods. The author has clearly devoted a lot of effort to pedagogical details, and the exposition is designed to effortlessly bring the beginning student up to speed in basic applications of the method.' Peter Olver, ZAMM'I really enjoyed reading this book and I am planning on using some parts for one of my next courses.' Monatshefte für Mathematik'… a nice introduction to symmetry methods for ordinary and partial differential equations written with passion by a specialist … after a few pages it becomes clear that the book is written in a lucid and precise manner.' Zentralblatt MATH'This new book by Peter Hydon … is eminently suitable for advanced undergraduates and beginning postgraduate students … Overall I thoroughly recommend this book and believe that it will be a useful textbook for introducing students to symmetry methods for differential equations.' Journal of Nonlinear Mathematical Physics'Throughout the text numerous examples are worked out in detail and the exercises have been well chosen. this is the most readable text on this material I have seen and I would recommend the book for self-study (as an introduction).' MathSciNet'It is very suitable for, and is specifically aimed at, postgraduate courses in the field. it is the more enjoyable for being written with infectious enthusiasm and there is a good selection of examples.' Mathematical GazetteTable of Contents1. Introduction to symmetries; 1.1. Symmetries of planar objects; 1.2. Symmetries of the simplest ODE; 1.3. The symmetry condition for first-order ODEs; 1.4. Lie symmetries solve first-order ODEs; 2. Lie symmetries of first order ODEs; 2.1. The action of Lie symmetries on the plane; 2.2. Canonical coordinates; 2.3. How to solve ODEs with Lie symmetries; 2.4. The linearized symmetry condition; 2.5. Symmetries and standard methods; 2.6. The infinitesimal generator; 3. How to find Lie point symmetries of ODEs; 3.1 The symmetry condition. 3.2. The determining equations for Lie point symmetries; 3.3. Linear ODEs; 3.4. Justification of the symmetry condition; 4. How to use a one-parameter Lie group; 4.1. Reduction of order using canonical coordinates; 4.2. Variational symmetries; 4.3. Invariant solutions; 5. Lie symmetries with several parameters; 5.1. Differential invariants and reduction of order; 5.2. The Lie algebra of point symmetry generators; 5.3. Stepwise integration of ODEs; 6. Solution of ODEs with multi-parameter Lie groups; 6.1 The basic method: exploiting solvability; 6.2. New symmetries obtained during reduction; 6.3. Integration of third-order ODEs with sl(2); 7. Techniques based on first integrals; 7.1. First integrals derived from symmetries; 7.2. Contact symmetries and dynamical symmetries; 7.3. Integrating factors; 7.4. Systems of ODEs; 8. How to obtain Lie point symmetries of PDEs; 8.1. Scalar PDEs with two dependent variables; 8.2. The linearized symmetry condition for general PDEs; 8.3. Finding symmetries by computer algebra; 9. Methods for obtaining exact solutions of PDEs; 9.1. Group-invariant solutions; 9.2. New solutions from known ones; 9.3. Nonclassical symmetries; 10. Classification of invariant solutions; 10.1. Equivalence of invariant solutions; 10.2. How to classify symmetry generators; 10.3. Optimal systems of invariant solutions; 11. Discrete symmetries; 11.1. Some uses of discrete symmetries; 11.2. How to obtain discrete symmetries from Lie symmetries; 11.3. Classification of discrete symmetries; 11.4. Examples.
£46.54
Cambridge University Press Advanced Mathematics for Applications
Book SynopsisAndrea Prosperetti draws on many years' experience at the forefront of research to produce a guide to the mathematical methods needed for classical fields. Each chapter is essentially self-contained, so users can fashion their own path through the material according to their needs.Trade Review'This carefully written book by a well-known expert in the area is also an excellent guide to the present literature, recommended as well to graduate students as to experts in the area. This volume will help the reader in getting acquainted with some mathematical aspects of the modern theory of linear and non-linear phenomena arising in relevant applications to mathematical physics.' Zentralblatt MATH'A truly wonderful book … The author succeeded in creating a new type of book, that many will put on their desks, and they should: beginners, physicists, advanced learners, instructors, users of maths in the sciences … A modern work, showing new ways, unusually multi-layered, applicable in many contexts and at many levels, an exciting book.' Siegfried Großmann, Philipps-Universität Marburg'This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together.' Laura K. Gross, SIAM ReviewTable of ContentsPreface; To the reader; List of tables; Part I. General Remarks and Basic Concepts: 1. The classical field equations; 2. Some simple preliminaries; Part II. Applications: 3. Fourier series: applications; 4. Fourier transform: applications; 5. Laplace transform: applications; 6. Cylindrical systems; 7. Spherical systems; Part III. Essential Tools: 8. Sequences and series; 9. Fourier series: theory; 10. The Fourier and Hankel transforms; 11. The Laplace transform; 12. The Bessel equation; 13. The Legendre equation; 14. Spherical harmonics; 15. Green's functions: ordinary differential equations; 16. Green's functions: partial differential equations; 17. Analytic functions; 18. Matrices and finite-dimensional linear spaces; Part IV. Some Advanced Tools: 19. Infinite-dimensional spaces; 20. Theory of distributions; 21. Linear operators in infinite-dimensional spaces; Appendix; References; Index.
£160.55
Cambridge University Press Solving Odes with MATLAB
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£42.74
Cambridge University Press Random Dynamical Systems
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£44.64
Cambridge University Press Topics in Dynamics and Ergodic Theory
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£61.71
Cambridge University Press Thinking about Ordinary Differential Equations
Thinking about Ordinary Differential Equations | BookCurl
£95.95
Cambridge University Press Thinking about Ordinary Differential Equations
Thinking about Ordinary Differential Equations | BookCurl
£41.79
Cambridge University Press Solitons
Book SynopsisThis 1999 book investigates the high degree of symmetry that lies hidden in integrable systems. Differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems.Trade Review' ... this charming book can be recommended to anybody interested in the modern development in the mathematics arising from mathematical physics.' EMSTable of ContentsPreface; 1. The KdV equation and its symmetries; 2. The KdV hierarchy; 3. The Hirota equation and vertex operators; 4. The calculus of Fermions; 5. The Boson–Fermion correspondence; 6. Transformation groups and tau functions; 7. The transformation group of the KdV equation; 8. Finite dimensional Grassmannians and Plücker relations; 9. Infinite dimensional Grassmannians; 10. The bilinear identity revisited; Solutions to exercises; Bibliography; Index.
£71.24
Cambridge University Press Computational Differential Equations
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£66.49
Cambridge University Press Harmonic Maps Loop Groups and Integrable Systems 38 London Mathematical Society Student Texts Series Number 38
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£100.70
Cambridge University Press Systems of Conservation Laws 1
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£136.80
Cambridge University Press Control Theory for Partial Differential Equations Volume 2 Abstract Hyperboliclike Systems over a Finite Time Horizon
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£133.95
Cambridge University Press LMSST 38 Harmonic Maps Loop Group London Mathematical Society Student Texts Series Number 38
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£43.69
Cambridge University Press LMS 255 Symmetries Integrability London Mathematical Society Lecture Note Series Series Number 255
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£61.71
Cambridge University Press Stochastic Flows and Stochastic Differential Equations 24 Cambridge Studies in Advanced Mathematics Series Number 24
Book SynopsisThe main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows. The classical theory was initiated by K. Ità and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby ItÃ's theory as a special case. The book can be used with advanced courses on probability theory or for self-study. The author begins with a discussion of Markov processes, martingales and Brownian motion, followed by a review of ItÃ's stochastic analysis. The next chapter deals with continuous semimartingales with spatial parameters, in order to study stochastic flow, and a generalisation of Ito's equation. Stochastic flows and their relation with this are generalised and considered in chapter 4. It is shown that solutions of a gTrade Review"The book could be used with advanced courses on probability theory or for self study." MTW, JASATable of Contents1. Stochastic processes and random fields; 2. Continuous semimartingales and stochastic integrals; 3. Semimartingales with spatial parameter and stochastic integrals; 4. Stochastic flows; 5. Convergence of stochastic flows; 6. Stochastic partial differential equations.
£71.24
Cambridge University Press Domain Decomposition
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£52.24
Cambridge University Press Asymptotic Expansions
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£37.99
Cambridge University Press InfiniteDimensional Dynamical Systems An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors 28 Cambridge Texts in Applied Mathematics Series Number 28
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£133.95
Cambridge University Press Systems of Conservation Laws 2
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£159.60
Cambridge University Press InfiniteDimensional Dynamical Systems
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£59.84
Cambridge University Press Dynamical Systems and Numerical Analysis
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£76.94
Cambridge University Press Holomorphic Dynamics 66 Cambridge Studies in Advanced Mathematics Series Number 66
Book SynopsisThis book, first published in 2000, emphasizes the substantial role played by classical complex analysis in understanding holomorphic dynamics and gives an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables, as well as the case of rational functions.Table of Contents1. The dynamics of polynomial maps; 2. Fatou and Julia sets; 3. Dynamics of entire functions; 4. Dynamics of rational functions; 5. Kleinian groups and Sullivan's dictionary; 6. The dynamics of holomorphic maps of sveral variables; 7. Dynamics of generalized Hénon maps; 8. Pluripotential theory of polynomial automorphisms; 9. Dynamics of polynomial automorphisms; Bibliography; Index.
£122.55
Cambridge University Press Strongly Elliptic Systems and Boundary Integral Equations
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£122.55
Cambridge University Press Strongly Elliptic Systems and Boundary Integral Equations
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£48.47
Cambridge University Press The NavierStokes Equations
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£61.71
Cambridge University Press Inequalities
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£52.24
Cambridge University Press Groups and Analysis The Legacy of Hermann Weyl 354 London Mathematical Society Lecture Note Series Series Number 354
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£79.10
Cambridge University Press Algebraic Theory of Differential Equations 357 London Mathematical Society Lecture Note Series Series Number 357
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£53.99
Cambridge University Press A First Course in the Numerical Analysis of Differential Equations 44 Cambridge Texts in Applied Mathematics Series Number 44
Book SynopsisNumerical 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 modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; aTrade Review'A well written and exciting book … the exposition throughout is clear and very lively. The author's enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.' Proceedings of the Edinburgh Mathematical Society'This is a well-written, challenging introductory text that addresses the essential issues in the development of effective numerical schemes for the solution of differential equations: stability, convergence, and efficiency. The soft cover edition is a terrific buy - I highly recommend it.' Mathematics of Computation'This book can be highly recommended as a basis for courses in numerical analysis.' Zentralblatt fur Mathematik'The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject.' Mathematical Reviews'… nicely crafted and full of interesting details.' ITW Nieuws'I believe this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations . . .' Computing Reviews'As a mathematician who developed an interest in numerical analysis in the middle of his professional career, I thoroughly enjoyed reading this text. I wish this book had been available when I first began to take a serious interest in computation. The author's style is comfortable . . . This book would be my choice for a text to 'modernize' such courses and bring them closer to the current practice of applied mathematics.' American Journal of Physics'Iserles has successfully presented, in a mathematically honest way, all essential topics on numerical methods for differential equations, suitable for advanced undergraduate-level mathematics students.' Georgios Akrivis, University of Ioannina, Greece'The present book can, because of the extension even more than the first edition, be highly recommended for readers from all fields, including students and engineers.' Zentralblatt MATHTable of ContentsPreface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary Differential Equations: 1. Euler's method and beyond; 2. Multistep methods; 3. Runge–Kutta methods; 4. Stiff equations; 5. Geometric numerical integration; 6. Error control; 7. Nonlinear algebraic systems; Part II. The Poisson Equation: 8. Finite difference schemes; 9. The finite element method; 10. Spectral methods; 11. Gaussian elimination for sparse linear equations; 12. Classical iterative methods for sparse linear equations; 13. Multigrid techniques; 14. Conjugate gradients; 15. Fast Poisson solvers; Part III. Partial Differential Equations of evolution: 16. The diffusion equation; 17. Hyperbolic equations; Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index.
£47.49
Cambridge University Press advancedmathematicsforapplications
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£54.14
Cambridge University Press Levy Processes and Stochastic Calculus 116 Cambridge Studies in Advanced Mathematics Series Number 116
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£76.94
Cambridge University Press Soliton Equations and their AlgebroGeometric Solutions Volume 1 11Dimensional Continuous Models Cambridge Studies in Advanced Mathematics Series Number 79
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£133.95
Cambridge University Press LMS 293 2nd Ord Pr Dif Equ Hilbert London Mathematical Society Lecture Note Series Series Number 293
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£67.51
Cambridge University Press Russian Literature Modernism and the Visual Arts Cambridge Studies in Russian Literature
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£50.99
Cambridge University Press Wavelets CaldernZygmund and Multilinear Operators 48 Cambridge Studies in Advanced Mathematics Series Number 48
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£72.19
Cambridge University Press Introduction to Dynamical Systems
Book SynopsisThis introduction to the subject of dynamical systems is ideal for a one-year graduate course. From chapter one, the authors use examples to motivate, clarify and develop the theory. The book rounds off with beautiful and remarkable applications to such areas as number theory, data storage, and Internet search engines.Trade Review'… an ideal choice for a graduate course on dynamical systems … warmly recommended …' Acta Scientiarum Mathematicarum'… exceptionally well written … You should consider adopting this wonderful text for your next graduate course on the pure mathematics of the modern theory of dynamical systems.' Carmen Chicone, SIAM Review'… despite the breadth, one finds here major results rigorously treated and substantial applications. By itself, the clean, accessible exposition of the amazing Sharkovsky theorem would justify the acquisition of this book … Highly recommended.' Choice'While the pace is fast and the book is very concise, the organization and selection of topics has been considered carefully, and the writing is strong enough to support the speedy treatment … It certainly does give a notion of the scope of dynamical systems in a way that few other single books do.' Bill Satzer, MAA ReviewsTable of ContentsIntroduction; 1. Examples and basic concepts; 2. Topological dynamics; 3. Symbolic dynamics; 4. Ergodic theory; 5. Hyperbolic dynamics; 6. Ergodicity of Anosov diffeomorphisms; 7. Low-dimensional dynamics; 8. Complex dynamics; 9. Measure-theoretic entropy; Bibliography; Index.
£59.84
Cambridge University Press Solving ODEs with MATLAB
Book SynopsisThis concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the code are discussed.Trade Review' … this is a readable, accessible text full of invaluable advice, illustrated using interesting examples and exercises … if you do have some background knowledge of numerical analysis, MATLAB, and are motivated by the application of numerical methods to real problems, you will find this book full of interest … the book acts as a useful introduction to several important, more general, issues in scientific computing.' The Mathematical GazetteTable of Contents1. Getting started; 2. Initial value problems; 3. Boundary value problems; 4. Delay differential equations.
£155.80
Cambridge University Press Random Dynamical Systems
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£57.95
Cambridge University Press The ThreeBody Problem
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£89.29
Cambridge University Press Theory of Orbit Determination
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£85.49
