Mathematical / Computational / Theoretical physics Books
Taylor & Francis Ltd Guide to Modern Physics
Book SynopsisThis is a how to guide for making beginning calculations in modern physics. The academic level is second year college physical science and engineering students. The calculations are performed in Mathematica, and stress graphical visualization, units, and numerical answers. The techniques show the student how to learn the physics without being hung up on the math. There is a continuing movement to introduce more advanced computational methods into lower-level physics courses. Mathematica is a unique tool in that code is written as human readable much like one writes a traditional equation on the board.Key Features:Concise summary of the physics concepts.Over 300 worked examples in Mathematica.Tutorial to allow a beginner to produce fast results.The companion code for this book can be found here:Table of Contents1. Basis of Modern Physics 2. Thermal Radiation 3. Key Processes 4. Special Relativity 5. Bohr Model 6. Particle in a Box 7. Quantum Harmonic Oscillator 8. Hydrogen Atom 9. Statistical Physics 10. Astrophysics Appendix A: Mathematica Starter Appendix B: Physical Constants
£43.99
Springer New York Numerical Approximation of Hyperbolic Systems of
Book SynopsisThis monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables.Table of ContentsNonlinear hyperbolic systems in one space dimension.- Gas dynamics and reacting flows.- Finite volume schemes for one-dimensional systems.- The case of multidimensional systems.- An introduction to boundary conditions.- Source terms.
£143.99
Cambridge University Press The Theory of Hardys ZFunction 196 Cambridge Tracts in Mathematics Series Number 196
Book SynopsisHardy's Z-function, related to the Riemann zeta-function Î(s), was originally utilised by G. H. Hardy to show that Î(s) has infinitely many zeros of the form +it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line +it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of Î(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research.Table of Contents1. Definition of ζ(s), Z(t) and basic notions; 2. The zeros on the critical line; 3. The Selberg class of L-functions; 4. The approximate functional equations for ζk(s); 5. The derivatives of Z(t); 6. Gram points; 7. The moments of Hardy's function; 8. The primitive of Hardy's function; 9. The Mellin transforms of powers of Z(t); 10. Further results on Mk(s)$ and Zk(s); 11. On some problems involving Hardy's function and zeta moments; References; Index.
£105.45
Cambridge University Press Manifolds Tensors and Forms
Book SynopsisProviding a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. It features over 250 detailed exercises and discusses a variety of applications.Table of ContentsPreface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
£64.99
Cambridge University Press The Cosmological Singularity
Book SynopsisWritten for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the BelinskiKhalatnikovLifshitz conjecture on this area of research.Trade Review'The present monograph is a carefully developed overview about the mathematical details of the big bang singularity, mainly within (but not restricted to) general relativity theory. Chapter 1 presents the basic structure of the singularity, including the Kasner-like and the oscillatory-like cases. Chapters 2 and 3 deal with the Bianchi models, especially the BLK-cases Bianchi VIII and IX and the chaotic character observed there. In chapter 4, the influence of matter and/or changed space-time dimension are discussed. Chapters 5 and 6 deal with the billiard representation of the dynamical system describing the approach to the singularity by a mathematical equivalence of the system of equations to the motion of a point particle in a region with boundary, where (like in the billiard game), the article is reflected at the boundary. This idea is formalized in chapter 7 by the introduction of the Coxeter group. The appendices are useful for several topics, e.g., the spinor field and the Kac-Moody algebra.' Hans-Jürgen Schmidt, Zentralblatt MATH'This monograph discusses at length the structure of the general solution of the Einstein equations with a cosmological singularity in Einstein-matter systems in four and higher space-time dimensions, starting from the fundamental work of Belinski (the book's lead author), Khalatnikov and Lifshitz (BKL) - published in 1969. … Quite technical and advanced, this book is meant for theoretical and mathematical physicists working on general relativity, supergravity and cosmology.' CERN CourierTable of ContentsPreface; 1. Introduction and outline; Part I. BKL Analysis: 2. Basic structure of cosmological singularity; 3. Homogeneous cosmological models; 4. On the cosmological chaos; 5. On the Inuence of matter and spacetime dimension; Part II. Cosmological Billiards: 6. The billiard of four-dimensional vacuum gravity; 7. General Cosmological Billiards; 8. Hyperbolic Coxeter groups; Appendix A. Various technical derivations; Appendix B. Homogeneous spaces and Bianchi classification; Appendix C. Spinor field; Appendix D. Lorentzian Kac-Moody algebras; References; Index.
£130.15
Cambridge University Press Berry Phases in Electronic Structure Theory
Book SynopsisA pedagogical introduction to a set of mathematical ideas associated with Berry phases that have revolutionized understanding of key aspects of the behavior of electrons in solids. Including practical examples and exercises throughout to test understanding, this book covers electric polarization, orbital magnetization and topological insulators.Trade Review'This book brings together almost forty years of progress in understanding how the wavefunctions of electrons in a crystal, and in particular their continuous evolution with momentum, determine important physical properties. David Vanderbilt is one of the creators of this field, and nearly every chapter includes topics where his contributions were decisive. In addition to its scope, one way in which this book differs from others on related topics is the clear path from physical insight, through theoretical understanding, to practical methods for specific materials. This book can be read profitably by those interested in the fundamental theory of topological phases as well as those seeking to understand modern electronic structure approaches.' Joel Moore, Chern-Simons Professor of Physics, University of California, Berkeley'The geometric phase and related concepts provide a unified framework for describing many fundamental properties of electrons in solids, from electric polarization to quantized effects in topological materials. Readers wishing to become familiar with these notions will find David Vanderbilt's excellent book to be an invaluable resource.' Ivo Souza, University of the Basque Country, San Sebastián'Berry phases and associated geometric and topological concepts have transformed our understanding of electronic properties. This book provides a much needed pedagogical exposition with computational instructions which will be very valuable for students and researchers in solid state physics and materials science.' Qian Niu, University of Texas'David Vanderbilt explicates a new exciting frontier in solid state physics and materials theory, and does so in a clear and interesting to read way. Not only does he cover every nook and cranny of this new area, but in the process clearly explains the basics of electronic structure theory, such as density functional theory (DFT) and tight-binding, that will be extremely useful and important to any student of condensed matter theory. The subject of the book is how the phases of the wave functions, neglected for decades, affect important measurable properties of materials. He covers everything from the mathematical theory of geometric phases, applications to polarization and orbital magnetism, all the way to complex applications such as three-dimensional topological insulators and beyond. To be able to write about such seemingly esoteric matters in such a clear and gripping way is the mark of a great teacher. I look forward to my second reading of the book!' Ronald Cohen, Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution for Science'For anyone who wants to learn about Berry phases in electronic structure and the exciting recent developments in topological insulators, I heartily recommend this book. David Vanderbilt is uniquely poised to present the concepts and practical developments in this field that has revolutionized our understanding of condensed matter. He has made some of the most important advances in electronic structure theory in the last twenty years, including the original work that has made Berry phases a central part the field, and he is known for lucid presentations. In this book Vanderbilt introduces the concepts in a way that is accessible to a nonexpert, with clear explanations and instructive examples, and yet he presents the material in the depth that it deserves. I recommend this book for anyone who wants to be a part of condensed matter theory in the twenty-first century or just to appreciate the basic ideas and phenomena of this exciting field.' Richard M. Martin, University of Illinois, Urbana Champaign'This is a well-structured book which will serve admirably as a text for advanced students as well as a means for more mature readers to gain an appreciation of the recent developments in this area of activity.' K. Alan Shore, Contemporary Physics'Its author, Rutgers University physicist David Vanderbilt, is eminently qualified for the task: he is the senior author of a large part of the research at the book's core. That literature is now fundamental knowledge for any scientist working on modern electronic structure. … The book's presentation combines mathematical rigor with illuminating discussions and examples … the ideal textbook for any special-topics course that broadly covers geometry and topology in electronic structure.' Physics Today'… I would like to recommend this book to crystallographers, and more generally to condensed-matter physicists who wish to learn about the physics of Berry phases. The pedagogical presentation used throughout will allow careful readers to start working on the more detailed literature with a solid basis and a clear view of recent results.' Laurent Chaput, Acta CrystallographicaTable of ContentsPreface; Acronyms; Introduction; 1. Invariance and quantization of charges and currents; 2. Review of electronic structure theory; 3. Berry phases and curvatures; 4. Electric polarization; 5. Topological insulators and semimetals; 6. Orbital magnetization and axion magnetoelectric coupling; Appendix A. Fourier transform conventions; Appendix B. Optimal alignment and the singular value decomposition; Appendix C. Gauge transformation of the Chern–Simons axion coupling; Appendix D. The PythTB package; References; Index.
£66.49
Cambridge University Press Theory of Simple Glasses
Book SynopsisThis pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.Trade Review'In this advanced textbook, the authors, all solid-state physicists, present a theory of simple glasses, defined as collections of interacting point particles. The approach, based on statistical mechanics and concepts of multiple-state metastability, is rigorous and educational. Derivations are careful and detailed … An especially useful and educational feature is that each chapter includes a résumé of main results and an annotated short bibliography geared to beginning students. An extensive, up-to-date bibliography at the end mainly draws from the Physical Review literature and related journals. Minimally indexed (no entries on shear stress or strain, viscosity, temperature, or spheres), the book is oriented toward advanced undergraduates or beginning graduate students (who will need preparation in statistical mechanics and liquid theory) and researchers in glasses, essentially addressing the solid-state physics and statistical mechanics communities.' J. Lambropoulos, ChoiceTable of ContentsPreface; 1. Infinite-dimensional models in statistical physics; 2. Atomic liquids in infinite dimensions: thermodynamics; 3. Atomic liquids in infinite dimensions: equilibrium dynamics; 4. Thermodynamics of glass states; 5. Replica symmetry breaking and hierarchical free energy landscapes; 6. The Gardner transition; 7. Counting glass states: the complexity; 8. Packing spheres in large dimensions; 9. The jamming transition; 10. Rheology of the glass; References; Index.
£999.99
Cambridge University Press Relativistic Figures of Equilibrium
Book SynopsisTreating the classical problem of gravitational physics, this book presents basic principles, deals with analytically tractable limiting cases, and considers the general case using powerful numerical methods. A valuable reference for researchers in general relativity, mathematical physics and astrophysics, it is accompanied by a website containing code.Trade ReviewReview of the hardback: '… this book is a very valuable tool for anybody wishing to learn more about relativistic rotating bodies in equilibrium. … overall it is an excellent reference on this topic.' Classical and Quantum GravityReview of the hardback: 'This is an advanced and specialised book, presenting the state of the art in this field, with emphasis on the authors' own expertise and approaches. It contains an extensive discussion of the analytical handling of limiting cases on the one hand and the numerical treatment of the general case on the other, thus providing a complete picture of the subject. … pleasant to read …This book is a standard reference for this subject every researcher in relativity theory should know.' General Relativity and GravitationReview of the hardback: 'Nicely produced by Cambridge University Press, this rather specialized book rich in analytical and numerical methods is of value to students and professional researchers in general relativity, mathematical physics and astrophysics.' Mathematical ReviewsTable of ContentsPreface; Notation; 1. Rotating fluid bodies in equilibrium: fundamental notions and equations; 2. Analytical treatment of limiting cases; 3. Numerical treatment of the general case; 4. Remarks on stability and astrophysical relevance; Appendixes; References; Index.
£43.99
Cambridge University Press Strong Interactions of Hadrons at High Energies
£58.89
Cambridge University Press A Students Guide to Waves Students Guides
Book SynopsisWaves are an important topic in the fields of mechanics, electromagnetism, and quantum theory, but many students struggle with the mathematical aspects. Written to complement course textbooks, this book focuses on the topics that students find most difficult. Retaining the highly popular approach used in Fleisch''s other Student''s Guides, the book uses plain language to explain fundamental ideas in a simple and clear way. Exercises and fully-worked examples help readers test their understanding of the concepts, making this an ideal book for undergraduates in physics and engineering trying to get to grips with this challenging subject. The book is supported by a suite of online resources available at www.cambridge.org/9781107643260. These include interactive solutions for every exercise and problem in the text and a series of video podcasts in which the authors explain the important concepts of every section of the book.Trade Review'I recommend this supplementary textbook as a clear tutorial for understanding the basic concepts of waves and the wave equation with its applications to mechanics, electromagnetic waves and the Schrӧdinger equation. … It is written for undergraduates in physics and engineering, but it also has exceptional value to a wider readership. … Physical insights that are helpful for a deep understanding of waves are uniquely presented. The text is supplemented with clear and useful graphs. The book's website contains additional resources: worked solutions to all problems, animated graphics, a few errata, and author podcasts to augment all the chapters.' Barry R. Masters, Optics and Photonics NewsTable of ContentsIntroduction; 1. Wave fundamentals; 2. The wave equation; 3. Wave components; 4. The mechanical wave equation; 5. The electromagnetic wave equation; 6. The quantum wave equation; References; Index.
£23.99
Cambridge University Press, India Experiment and Theory in Physics
Book SynopsisOriginally published in 1943, this book presents an expanded version of an address given by Max Born gave to the Durham Philosophical Society and the Pure Science Society. The text provides an examination of the mutual relationship between theory and experiment in the development of physics.
£10.91
Cambridge University Press Mathematical and Physical Papers Volume 1
Book SynopsisThis collection brings together in six volumes the published articles of the eminent mathematical physicist and engineer William Thomson, first Baron Kelvin (18241907). Topics covered include heat, electricity, magnetism and electrotelegraphy, hydrodynamics, tidal theory and navigation.Table of Contents; .
£48.99
Cambridge University Press Essential Statistical Physics
Book SynopsisThis clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville''s Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challengingTrade Review'At last a textbook that contains all the required elements for a modern advanced undergraduate course on statistical physics: foundations, quantum statistical mechanics, phase transitions and dynamics. I particularly like the derivation of ensembles through maximization of Gibbs entropy and the Langevin description of Brownian motion. Plenty of instructive problems within ten digestible chapters make this a text I can recommend to my students.' Martin Evans, University of Edinburgh'Statistical mechanics is a vast and fascinating topic, sometimes intimidating beginning students. Kennett succeeds in delivering an agile, fresh and modern exposition of the essential ideas and methods, in addition to a well-thought selection of examples and applications borrowed from all branches of physics. Students and teachers alike will enjoy the carefully organized table of contents for self-study and lecture preparation.' Roberto Raimondi, Roma Tre University'This book incorporates, into a single course, ideas and theoretical techniques in statistical physics and quantum mechanics that are connected by the physical phenomena they are meant to describe. Yet they are rarely all found in the same text. Professor Kennett offers students of theoretical physics a rare opportunity to acquire a mature understanding of their impact and meaning.' Herbert Fertig, Indiana University, BloomingtonTable of ContentsPreface; 1. Introduction; 2. The microcanonical ensemble; 3. Liouville's theorem; 4. The canonical ensemble; 5. Kinetic theory; 6. The grand canonical ensemble; 7. Quantum statistical mechanics; 8. Fermions; 9. Bosons; 10. Phase transitions and order; Appendix A Gaussian integrals and stirling's formula; Appendix B Primer on thermal physics; Appendix C Heat capacity cusp in Bose systems; References; Index.
£31.34
Cambridge University Press Quantum Field Theory
Book SynopsisQuantum field theory (QFT), the language of particle physics, is crucial to a physicist''s graduate education. Based on lecture notes for courses taught for many years at Radboud University in the Netherlands, this book presents an alternative approach to teaching QFT using Feynman diagrams. A diagrammatic approach to understanding QFT exposes young physicists to an orthogonal introduction to the theory, bringing new ways to understand challenges in the field. Diagrammatic techniques using Feynman diagrams are used didactically, starting from simple discussions in lower dimensions to more complex topics in the Standard Model. Worked examples and exercises, for which solutions are available online, help the reader develop a deep understanding and intuition that enhances their problem-solving skills and understanding of QFT. Classroom-tested, this accessible book is valuable resource for graduate students and researchers.Trade Review'Highly recommended.' E. Kincanon, Choice MagazineTable of ContentsPreface. 1. QFT in zero dimensions; 2. Loop expansion and the effective action; 3. On renormalization; 4. More fields in zero dimensions; 5. QFT in Euclidean spaces; 6. QFT in Minkowski space; 7. Scattering processes; 8. Introduction to loop calculations; 9. More on renormalization; 10. Dirac particles; 11. Helicity techniques for Dirac particles; 12. Vector particles; 13. Quantum electrodynamics; 14. Higher-order effects in QED; 15. Quantum chromodynamics; 16. Higher-order effects in QCD; 17. Electroweak theory; 18. More example computations; Appendices.
£56.99
Cambridge University Press Field Theory of NonEquilibrium Systems
Book SynopsisThis book provides a detailed presentation of modern non-equilibrium field-theoretical methods, applied to examples ranging from biophysics to the kinetics of superfluids and superconductors. Suitable for graduate students and researchers in condensed matter physics, this new edition includes updated content and problems throughout.Trade ReviewPraise for the first edition 'Field Theory of Non-Equilibrium Systems, written by theoretical condensed-matter physicist Alex Kamenev, is a lively pedagogical exposition of the Keldysh technique based on functional integration … It is meant for advanced graduate students and professionals who have not had prior exposure to the technique but would like to learn it. Experts in the field may also enjoy the diversity of the subjects covered and the clarity with which they are presented. Thanks to those features, Field Theory of Non-Equilibrium Systems is a welcome introduction to the field and could well become a classic.' Vojkan Jaksic, Physics TodayTable of Contents1. Introduction; Part I. Systems with Few Degrees of Freedom: 2. Bosons; 3. Single-particle quantum mechanics; 4. Classical stochastic systems; 5. Driven-dissipative systems; Part II. Bosonic and Classical Fields: 6. Bosonic fields; 7. Dynamics of collisionless plasma; 8. Kinetics of Bose condensates; 9. Dynamics of phase transitions; Part III. Fermions: 10. Fermions; 11. Kinetic theory and hydrodynamics; 12. Aspects of kinetic theory; 13. Quantum transport; Part IV. Disordered Metals and Superconductors: 14. Disordered fermionic systems; 15. Mesoscopic effects; 16. Electron–electron interactions in disordered metals; 17. Dynamics of disordered superconductors; 18. Electron–phonon interactions; References; Index.
£69.99
Cambridge University Press Advanced Topics in Quantum Mechanics
Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the WentzelKramersBrillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner''s phase space formulation and Feynman''s path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throu
£54.99
Cambridge University Press Semigroups of Linear Operators
Book SynopsisThe theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of HilleYosida and LumerPhillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and FellerMarkov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the RiemannLiouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequTrade Review'… Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews'Experts can quickly browse through any of the chapters, and get nicely acquainted with examples they are not yet fully aware of. Students can read this book fairly casually, and gain great motivation to study functional, stochastic, and/or harmonic analysis further. Last but not least, teachers of graduate courses can design several great courses by elaborating on one of the many threads running through the book under review and using the referred sources to turn them into self-contained stories. All will appreciate the book's excellent mix of erudition and pedagogy.' Pierre Portal, MathSciNet'Some readers will enjoy the topic for its inherent attraction as a means of presenting results in a simple and widely applicable way. A masters student who is interested in researching in analysis but not in technical details of PDEs may nd this text particularly useful for finding a research topic in one of the related areas. In these respects the book achieves the aims declared in its introduction, in a way which is not found in earlier texts.' Charles Batty, The Mathematical Gazette'This excellent book, supplementing the known texts on operator semigroups, stems from the author's lectures for students with basic knowledge of functional analysis and measure theory … the book totally meets the goals of the LMS Student Texts series and is highly recommended to the University community.' Andrey V. Bulinski, zbMATHTable of ContentsIntroduction; 1. Semigroups and generators; 2. The generation of semigroups; 3. Convolution semigroups of measures; 4. Self adjoint semigroups and unitary groups; 5. Compact and trace class semigroups; 6. Perturbation theory; 7. Markov and Feller semigroups; 8. Semigroups and dynamics; 9. Varopoulos semigroups; Notes and further reading; Appendices: A. The space C0(Rd); B. The Fourier transform; C. Sobolev spaces; D. Probability measures and Kolmogorov's theorem on construction of stochastic processes; E. Absolute continuity, conditional expectation and martingales; F. Stochastic integration and Itô's formula; G. Measures on locally compact spaces: some brief remarks; References; Index.
£36.48
Cambridge University Press WignerType Theorems for Hilbert Grassmannians
Book SynopsisWigner''s theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.Table of ContentsIntroduction; 1. Two lattices; 2. Geometric transformations of Grassmannians; 3. Lattices of closed subspaces; 4. Wigner's theorem and its generalizations; 5. Compatibility relation; 6. Applications; References; Index.
£54.87
Cambridge University Press Constrained Willmore Surfaces
Book SynopsisFrom Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed compTable of ContentsIntroduction; 1. A bundle approach to conformal surfaces in space-forms; 2. The mean curvature sphere congruence; 3. Surfaces under change of flat metric connection; 4. Willmore surfaces; 5. The Euler–Lagrange constrained Willmore surface equation; 6. Transformations of generalized harmonic bundles and constrained Willmore surfaces; 7. Constrained Willmore surfaces with a conserved quantity; 8. Constrained Willmore surfaces and the isothermic surface condition; 9. The special case of surfaces in 4-space; Appendix A. Hopf differential and umbilics; Appendix B. Twisted vs. untwisted Bäcklund transformation parameters; References; Index.
£55.09
Cambridge University Press GinzburgLandau Theory of Condensates
Book SynopsisGinzburgLandau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to GinzbergLandau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.Trade Review'Baruch Rosenstein and Dingping Li, renowned experts in the theory of superconductivity, will guide readers, like Dante's Virgil, through the circles of the fascinating world of Topological Matter.' Andrey Varlamov, CNR-SPIN and University of Tor VergataTable of ContentsPreface. 1. Introduction and overview; Part I. Ordered Phases of Condensed Matter Disrupted by Topological Defects: 2. The phenomenological (Landau) description of the ordered condensed matter from magnets to Bose condensates; 3. Simplest topological defects; 4. Topological defects and their classification; Part II. Structure of the Topological Matter Created by Gauge Field: 5. Repulsion between solitons and viable vortex matter created by a gauge field; 6. Abrikosov vortices created by the magnetic field; 7. Structure and magnetization of the vortex lattice within London approximation; 8. Structure and megnetization of the vortex lattice within Abrikosov approximation; Part III. Excitation Modes of Condensate: Elasticity and Stability of the Topological Matter: 9. Linear stability analysis of the homogenous states; 10. Stability and the excitation spectrum of the single soliton and the vortex lattice; 11. Forces of solitons, pinning and elasticity of the vortex matter; Part IV. Dynamics of Condensates and Solitary Waves: 12. Dynamics of the order parameter field; 13. Solitary waves; 14. Viscous flow of the Abrikosov flux lattice; Part V. Thermal Fluctuations. 15. Statistical physics of mesoscopic degrees of freedom; 16. The Landau-Wilson approach to statistical physics of the interacting field fluctuations; 17. Thermal fluctuations in the vortex matter; Appendix; Index.
£56.69
Cambridge University Press The General Theory of Relativity
Book SynopsisThe book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein''s field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.Table of ContentsPreface; Acknowledgement; 1. Tensor calculus – a brief overview; 2. Geodesics; 3. Einstein field equations; 4. Linearized gravity; 5. Lie derivatives and Killing's equation; 6. Spacetimes of spherically symmetric distribution of matter and black holes; 7. Particle and photon orbits in the Schwarzschild spacetime; 8. Causal structure of spacetime; 9. Exact solutions of Einstein equations and their causal structures; 10. Rotating Black holes; 11. Elementary cosmology; 12. Elementary astrophysics; Appendix A. Extrinsic curvature; Appendix B. Lagrangian formalism of general relativity; Appendix C. 3+1 decomposition; Bibliography; Index.
£52.24
Cambridge University Press Classical and Quantum Statistical Physics
Statistical physics examines the collective properties of large ensembles of particles, and is a powerful theoretical tool with important applications across many different scientific disciplines. This book provides a detailed introduction to classical and quantum statistical physics, including links to topics at the frontiers of current research. The first part of the book introduces classical ensembles, provides an extensive review of quantum mechanics, and explains how their combination leads directly to the theory of Bose and Fermi gases. This allows a detailed analysis of the quantum properties of matter, and introduces the exotic features of vacuum fluctuations. The second part discusses more advanced topics such as the two-dimensional Ising model and quantum spin chains. This modern text is ideal for advanced undergraduate and graduate students interested in the role of statistical physics in current research. 140 homework problems reinforce key concepts and further develop read
£54.99
Cambridge University Press Problems in Quantum Field Theory
Book SynopsisThis collection of problems in Quantum Field Theory, accompanied by their complete solutions, aims to bridge the gap between learning the foundational principles and applying them practically. The carefully chosen problems cover a wide range of topics, starting from the foundations of Quantum Field Theory and the traditional methods in perturbation theory, such as LSZ reduction formulas, Feynman diagrams and renormalization. Separate chapters are devoted to functional methods (bosonic and fermionic path integrals; worldline formalism), to non-Abelian gauge theories (Yang-Mills theory, Quantum Chromodynamics), to the novel techniques for calculating scattering amplitudes and to quantum field theory at finite temperature (including its formulation on the lattice, and extensions to systems out of equilibrium). The problems range from those dealing with QFT formalism itself to problems addressing specific questions of phenomenological relevance, and they span a broad range in difficulty, for graduate students taking their first or second course in QFT.Trade Review'… a valuable bridge between textbook treatments and the modern literature and is an example of the type of volume often reported to be missing from the shelves. Libraries that serve universities teaching quantum field theory, or any institution with active research programs involving quantum field theory, should acquire this book ... Recommended.' M. C. Ogilvie, Choice ConnectTable of ContentsPreface; Acknowledgements; Notations and Conventions; Part I. Quantum Field Theory Basics; Part II. Functional Methods; Part III. Non-Abelian Fields; Part IV. Scattering Amplitudes; Part V. Lattice, Finite T, Strong Fields; Index.
£39.89
John Wiley & Sons Inc Quantum Information and Computation for Chemistry
Book SynopsisExamines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research wTable of ContentsCONTRIBUTORS TO VOLUME 154 v FOREWORD ix PREFACE TO THE SERIES xiii INTRODUCTION TO QUANTUM INFORMATION AND COMPUTATION FOR CHEMISTRY 1 By Sabre Kais BACK TO THE FUTURE: A ROADMAP FOR QUANTUM SIMULATION FROM VINTAGE QUANTUM CHEMISTRY 39 By Peter J. Love INTRODUCTION TO QUANTUM ALGORITHMS FOR PHYSICS AND CHEMISTRY 67 By Man-Hong Yung, James D. Whitfield, Sergio Boixo, David G. Tempel, and Alan Aspuru-Guzik QUANTUM COMPUTING APPROACH TO NONRELATIVISTIC AND RELATIVISTIC MOLECULAR ENERGY CALCULATIONS 107 By Libor Veis and Jiri Pittner DENSITY FUNCTIONAL THEORY AND QUANTUM COMPUTATION 137 By Frank Gaitan and Franco Nori QUANTUM ALGORITHMS FOR CONTINUOUS PROBLEMS AND THEIR APPLICATIONS 151 By A. Papageorgiou and J. F. Traub ANALYTIC TIME EVOLUTION, RANDOM PHASE APPROXIMATION, AND GREEN FUNCTIONS FOR MATRIX PRODUCT STATES 179 By Jesse M. Kinder, Claire C. Ralph, and Garnet Kin-Lic Chan FEW-QUBIT MAGNETIC RESONANCE QUANTUM INFORMATION PROCESSORS: SIMULATING CHEMISTRY AND PHYSICS 193 By Ben Criger, Daniel Park, and Jonathan Baugh PHOTONIC TOOLBOX FOR QUANTUM SIMULATION 229 By Xiao-Song Ma, Borivoje Daki´c, and Philip Walther PROGRESS IN COMPENSATING PULSE SEQUENCES FOR QUANTUM COMPUTATION 241 By J. True Merrill and Kenneth R. Brown REVIEW OF DECOHERENCE-FREE SUBSPACES, NOISELESS SUBSYSTEMS, AND DYNAMICAL DECOUPLING 295 By Daniel A. Lidar FUNCTIONAL SUBSYSTEMS AND STRONG CORRELATION IN PHOTOSYNTHETIC LIGHT HARVESTING 355 By David A. Mazziotti and Nolan Skochdopole VIBRATIONAL ENERGY TRANSFER THROUGH MOLECULAR CHAINS: AN APPROACH TOWARD SCALABLE INFORMATION PROCESSING 371 By C. Gollub, P. von den Hoff, M. Kowalewski, U. Troppmann, and R. de Vivie-Riedle ULTRACOLD MOLECULES: THEIR FORMATION AND APPLICATION TO QUANTUM COMPUTING 403 By Robin Cote DYNAMICS OF ENTANGLEMENT IN ONE- AND TWO-DIMENSIONAL SPIN SYSTEMS 449 By Gehad Sadiek, Qing Xu, and Sabre Kais FROM TOPOLOGICAL QUANTUM FIELD THEORY TO TOPOLOGICAL MATERIALS 509 By Paul Watts, Graham Kells, and Jiri Vala TENSOR NETWORKS FOR ENTANGLEMENT EVOLUTION 567 By Sebastian Meznaric and Jacob Biamonte AUTHOR INDEX 581 SUBJECT INDEX 615
£161.95
John Wiley & Sons Inc Advances in Chemical Physics Volume 155
Book SynopsisDiscusses aspects of the state of diverse subjects in chemical physics and related fields, with chapters written by top researchers in the field. This title provides the space needed for readers to grasp the topic, including fundamentals, discoveries, applications, and emerging avenues of research.Table of ContentsCONTRIBUTORS TO VOLUME 155 v PREFACE TO THE SERIES vii MODELING VIRAL CAPSID ASSEMBLY 1 By Michael F. Hagan CHARGES AT AQUEOUS INTERFACES: DEVELOPMENT OF COMPUTATIONAL APPROACHES IN DIRECT CONTACT WITH EXPERIMENT 69 By Robert Vácha, Frank Uhlig, and Pavel Jungwirth SOLUTE PRECIPITATE NUCLEATION: A REVIEW OF THEORY AND SIMULATION ADVANCES 97 By Vishal Agarwal and Baron Peters WATER IN THE LIQUID STATE: A COMPUTATIONAL VIEWPOINT 161 By Toshiko Ichiye CONSTRUCTION OF ENERGY FUNCTIONS FOR LATTICE HETEROPOLYMER MODELS: EFFICIENT ENCODINGS FOR CONSTRAINT SATISFACTION PROGRAMMING AND QUANTUM ANNEALING 201 By Ryan Babbush, Alejandro Perdomo-Ortiz, Bryan O’Gorman, William Macready, and Alan Aspuru-Guzik AUTHOR INDEX 245 SUBJECT INDEX 271
£157.45
John Wiley & Sons Inc Physics I 501 Practice Problems For Dummies Free
Book SynopsisOvercome your study inertia and polish your knowledge of physics Physics I: 501 Practice Problems For Dummies gives you 501 opportunities to practice solving problems from all the major topics covered you Physics I classin the book and online! Get extra help with tricky subjects, solidify what you've already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will help you succeed in this tough-but-required class, no matter what your skill level. Thanks to Dummies, you have a resource to help you put key concepts into practice. Work through practice problems on all Physics I topics covered in school classesStep through detailed solutions to build your understandingAccess practice questions online to study anywhere, any timeImprove your grade and up your study game with practice, practice, practiceThe material presented in Physics I: 501 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement Physics I instruction. Physics I: 501 Practice Problems For Dummies (9781119883715) was previously published as Physics I Practice Problems For Dummies (9781118853153). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsPart 1: The Questions 5 Chapter 1: Reviewing Math Fundamentals and Physics Measurements 7 Chapter 2: Moving along with Kinematics 11 Chapter 3: Moving in a Two-Dimensional World 17 Chapter 4: Pushing and Pulling: The Forces around You 23 Chapter 5: Slipping and Sliding: Motion and Forces 31 Chapter 6: Describing Rotational Motion 39 Chapter 7: Rotating Around in Different Loops 45 Chapter 8: Going with the Flow: Fluids 51 Chapter 9: Getting Some Work Done 57 Chapter 10: Picking Up Some Momentum with Impulse 65 Chapter 11: Rolling Around with Rotational Kinetics and Dynamics 73 Chapter 12: Bouncing with a Spring: Simple Harmonic Motion 87 Chapter 13: Heating Up with Thermodynamics and Heat Transfer 93 Chapter 14: Living in an Ideal World with the Ideal Gas Law 99 Chapter 15: Experiencing the Laws of Thermodynamics 103 Part 2: The Answers 109 Chapter 16: Answers 111 Index 413
£18.69
John Wiley & Sons Inc Statistical Physics
Book SynopsisThis undergraduate textbook provides students with a statistical mechanical foundation to the classical laws of thermodynamics through a comprehensive treatment of the basics of classical thermodynamics, equilibrium statistical mechanics, irreversible thermodynamics, and statistical mechanics of non-equilibrium phenomena.Trade Review“Summing Up: Recommended. Upper-division undergraduates.” (Choice, 1 March 2014) “The best choice is finally that the entropy is uncertainty commodified". The reviewer believes that the aim of the book is evident and it is worthwhile to make a detailed study of it from time to time.” (Zentralblatt MATH, 1 October 2013)Table of ContentsPreface xiii 1. Disorder or Uncertainty? 1 2. Classical Thermodynamics 5 2.1 The Classical Laws of Thermodynamics 5 2.2 Macroscopic State Variables and Thermodynamic Processes 6 2.3 Properties of the Ideal Classical Gas 8 2.4 Thermodynamic Processing of the Ideal Gas 10 2.5 Entropy of the Ideal Gas 13 2.6 Entropy Change in Free Expansion of an Ideal Gas 15 2.7 Entropy Change due to Nonquasistatic Heat Transfer 17 2.8 Cyclic Thermodynamic Processes, the Clausius Inequality and Carnot’s Theorem 19 2.9 Generality of the Clausius Expression for Entropy Change 21 2.10 Entropy Change due to Nonquasistatic Work 23 2.11 Fundamental Relation of Thermodynamics 25 2.12 Entropy Change due to Nonquasistatic Particle Transfer 28 2.13 Entropy Change due to Nonquasistatic Volume Exchange 30 2.14 General Thermodynamic Driving 31 2.15 Reversible and Irreversible Processes 32 2.16 Statements of the Second Law 33 2.17 Classical Thermodynamics: the Salient Points 35 Exercises 35 3. Applications of Classical Thermodynamics 37 3.1 Fluid Flow and Throttling Processes 37 3.2 Thermodynamic Potentials and Availability 39 3.2.1 Helmholtz Free Energy 40 3.2.2 Why Free Energy? 43 3.2.3 Contrast between Equilibria 43 3.2.4 Gibbs Free Energy 44 3.2.5 Grand Potential 46 3.3 Maxwell Relations 47 3.4 Nonideal Classical Gas 48 3.5 Relationship between Heat Capacities 49 3.6 General Expression for an Adiabat 50 3.7 Determination of Entropy from a Heat Capacity 50 3.8 Determination of Entropy from an Equation of State 51 3.9 Phase Transitions and Phase Diagrams 52 3.9.1 Conditions for Coexistence 53 3.9.2 Clausius–Clapeyron Equation 55 3.9.3 The Maxwell Equal Areas Construction 57 3.9.4 Metastability and Nucleation 59 3.10 Work Processes without Volume Change 59 3.11 Consequences of the Third Law 60 3.12 Limitations of Classical Thermodynamics 61 Exercises 62 4. Core Ideas of Statistical Thermodynamics 65 4.1 The Nature of Probability 65 4.2 Dynamics of Complex Systems 68 4.2.1 The Principle of Equal a Priori Probabilities 68 4.2.2 Microstate Enumeration 71 4.3 Microstates and Macrostates 72 4.4 Boltzmann’s Principle and the Second Law 75 4.5 Statistical Ensembles 77 4.6 Statistical Thermodynamics: the Salient Points 78 Exercises 79 5. Statistical Thermodynamics of a System of Harmonic Oscillators 81 5.1 Microstate Enumeration 81 5.2 Microcanonical Ensemble 83 5.3 Canonical Ensemble 84 5.4 The Thermodynamic Limit 88 5.5 Temperature and the Zeroth Law of Thermodynamics 91 5.6 Generalisation 91 Exercises 92 6. The Boltzmann Factor and the Canonical Partition Function 95 6.1 Simple Applications of the Boltzmann Factor 95 6.1.1 Maxwell–Boltzmann Distribution 95 6.1.2 Single Classical Oscillator and the Equipartition Theorem 97 6.1.3 Isothermal Atmosphere Model 98 6.1.4 Escape Problems and Reaction Rates 99 6.2 Mathematical Properties of the Canonical Partition Function 99 6.3 Two-Level Paramagnet 101 6.4 Single Quantum Oscillator 103 6.5 Heat Capacity of a Diatomic Molecular Gas 104 6.6 Einstein Model of the Heat Capacity of Solids 105 6.7 Vacancies in Crystals 106 Exercises 108 7. The Grand Canonical Ensemble and Grand Partition Function 111 7.1 System of Harmonic Oscillators 111 7.2 Grand Canonical Ensemble for a General System 115 7.3 Vacancies in Crystals Revisited 116 Exercises 117 8. Statistical Models of Entropy 119 8.1 Boltzmann Entropy 119 8.1.1 The Second Law of Thermodynamics 120 8.1.2 The Maximum Entropy Macrostate of Oscillator Spikiness 122 8.1.3 The Maximum Entropy Macrostate of Oscillator Populations 122 8.1.4 The Third Law of Thermodynamics 126 8.2 Gibbs Entropy 127 8.2.1 Fundamental Relation of Thermodynamics and Thermodynamic Work 129 8.2.2 Relationship to Boltzmann Entropy 130 8.2.3 Third Law Revisited 131 8.3 Shannon Entropy 131 8.4 Fine and Coarse Grained Entropy 132 8.5 Entropy at the Nanoscale 133 8.6 Disorder and Uncertainty 134 Exercises 135 9. Statistical Thermodynamics of the Classical Ideal Gas 137 9.1 Quantum Mechanics of a Particle in a Box 137 9.2 Densities of States 138 9.3 Partition Function of a One-Particle Gas 140 9.4 Distinguishable and Indistinguishable Particles 141 9.5 Partition Function of an N -Particle Gas 145 9.6 Thermal Properties and Consistency with Classical Thermodynamics 146 9.7 Condition for Classical Behaviour 147 Exercises 149 10. Quantum Gases 151 10.1 Spin and Wavefunction Symmetry 151 10.2 Pauli Exclusion Principle 152 10.3 Phenomenology of Quantum Gases 153 Exercises 154 11. Boson Gas 155 11.1 Grand Partition Function for Bosons in a Single Particle State 155 11.2 Bose–Einstein Statistics 156 11.3 Thermal Properties of a Boson Gas 158 11.4 Bose–Einstein Condensation 161 11.5 Cooper Pairs and Superconductivity 166 Exercises 167 12. Fermion Gas 169 12.1 Grand Partition Function for Fermions in a Single Particle State 169 12.2 Fermi–Dirac Statistics 170 12.3 Thermal Properties of a Fermion Gas 171 12.4 Maxwell–Boltzmann Statistics 173 12.5 The Degenerate Fermion Gas 176 12.6 Electron Gas in Metals 177 12.7 White Dwarfs and the Chandrasekhar Limit 179 12.8 Neutron Stars 182 12.9 Entropy of a Black Hole 183 Exercises 184 13. Photon Gas 187 13.1 Electromagnetic Waves in a Box 187 13.2 Partition Function of the Electromagnetic Field 189 13.3 Thermal Properties of a Photon Gas 191 13.3.1 Planck Energy Spectrum of Black-Body Radiation 191 13.3.2 Photon Energy Density and Flux 193 13.3.3 Photon Pressure 193 13.3.4 Photon Entropy 194 13.4 The Global Radiation Budget and Climate Change 195 13.5 Cosmic Background Radiation 197 Exercises 198 14. Statistical Thermodynamics of Interacting Particles 201 14.1 Classical Phase Space 201 14.2 Virial Expansion 203 14.3 Harmonic Structures 206 14.3.1 Triatomic Molecule 207 14.3.2 Einstein Solid 208 14.3.3 Debye Solid 209 Exercises 211 15. Thermodynamics away from Equilibrium 213 15.1 Nonequilibrium Classical Thermodynamics 213 15.1.1 Energy and Particle Currents and their Conjugate Thermodynamic Driving Forces 213 15.1.2 Entropy Production in Constrained and Evolving Systems 218 15.2 Nonequilibrium Statistical Thermodynamics 220 15.2.1 Probability Flow and the Principle of Equal a Priori Probabilities 220 15.2.2 The Dynamical Basis of the Principle of Entropy Maximisation 222 Exercises 223 16. The Dynamics of Probability 225 16.1 The Discrete Random Walk 225 16.2 Master Equations 226 16.2.1 Solution to the Random Walk 228 16.2.2 Entropy Production during a Random Walk 229 16.3 The Continuous Random Walk and the Fokker–Planck Equation 230 16.3.1 Wiener Process 232 16.3.2 Entropy Production in the Wiener Process 233 16.4 Brownian Motion 235 16.5 Transition Probability Density for a Harmonic Oscillator 236 Exercises 238 17. Fluctuation Relations 241 17.1 Forward and Backward Path Probabilities: a Criterion for Equilibrium 241 17.2 Time Asymmetry of Behaviour and a Definition of Entropy Production 243 17.3 The Relaxing Harmonic Oscillator 245 17.4 Entropy Production Arising from a Single Random Walk 247 17.5 Further Fluctuation Relations 249 17.6 The Fundamental Basis of the Second Law 253 Exercises 253 18. Final Remarks 255 Further Reading 261 Index 263
£41.36
Taylor & Francis Ltd Knot Theory
Book SynopsisOver the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text.Knot Theory, Second Edition is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.Trade ReviewPraise for the first editionThis book is highly recommended for all students and researchers in knot theory, and to those in the sciences and mathematics who would like to get a flavor of this very active field.”-Professor Louis H. Kauffman, Department of Mathematics, Statistics and Com-puter Science, University of Illinois at ChicagoTable of ContentsKnots, links, and invariant polynomials. Introduction. Reidemeister moves. Knot arithmetics. Links in 2-surfaces in R3.Fundamental group; the knot group. The knot quandle and the Conway algebra. Kauffman's approach to Jones polynomial. Properties of Jones polynomials. Khovanov's complex. Theory of braids. Braids, links and representations of braid groups. Braids and links. Braid construction algorithms. Algorithms of braid recognition. Markov's theorem; the Yang-Baxter equation. Vassiliev's invariants. Definition and Basic notions of Vassiliev invariant theory. The chord diagram algebra. The Kontsevich integral and formulae for the Vassiliev invariants. Atoms and d-diagrams. Atoms, height atoms and knots. The bracket semigroup of knots. Virtual knots. Basic definitions and motivation. Invariant polynomials of virtual links. Generalised Jones-Kauffman polynomial. Long virtual knots and their invariants. Virtual braids. Other theories. 3-manifolds and knots in 3-manifolds. Legendrian knots and their invariants. Independence of Reidemeister moves.
£114.00
Cambridge University Press Attractors of Hamiltonian Nonlinear Partial
Book SynopsisThis monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh''s convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.Table of ContentsIntroduction; 1. Global attraction to stationary states; 2. Global attraction to solitons; 3. Global attraction to stationary orbits; 4. Asymptotic stability of stationary orbits and solitons; 5. Adiabatic effective dynamics of solitons; 6. Numerical simulation of solitons; 7. Dispersive decay; 8. Attractors and quantum mechanics; References; Index.
£90.25
Cambridge University Press A Students Guide to General Relativity
Book SynopsisThis compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn''t shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein''s theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein''s equations of general relativity. The book is supported by numerous worked exampled and problems, and imTrade Review'The strength of Gray's book lies in his concern to provide friendly, pedagogical explanations for many tricky features of the theory, starting from a basic level, and his informal style will be welcomed by the less confident reader.' Peter J. Bussey, Contemporary Physics'... this book marks a welcome move to shorter, more focussed introductions to General Relativity aimed at undergraduate students. As the mathematical half of a full GR course it works well, but perhaps a less abstract approach and greater emphasis on the geometrical nature of the theory might appeal more to some readers.' Andrew Taylor, The Observatory'This book is part of the Cambridge 'Student's Guide' series. It is based on a 10 lecture course the author taught at the University of Glasgow. The book is mostly about introducing the math needed to reach the discussion of the Einstein equation.' Jorge Pullin, zbMATHTable of ContentsPreface; 1. Introduction; 2. Vectors, tensors and functions; 3. Manifolds, vectors and differentiation; 4. Energy, momentum and Einstein's equations; Appendix A. Special relativity – a brief introduction; Appendix B. Solutions to Einstein's equations; Appendix C. Notation; Bibliography; Index.
£19.99
John Wiley & Sons Inc Numerical Calculations in Clifford Algebra
Book SynopsisNUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA An intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. Applications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of paTable of ContentsList of Figures xv List of Tables xix Preface xxi Part I Entities and Operations 1 1 Introduction 3 1.1 Operations 3 1.2 History 4 1.3 Alternative Forms 5 1.4 Naming 6 1.5 Structure 7 1.5.1 Algebraic 7 1.5.2 Numeric 8 1.6 Entities 11 References 12 2 Input 13 2.1 Syntax 13 2.2 Constants 14 2.2.1 Specific Types 14 2.2.2 General 16 2.3 Variables 19 2.3.1 Checking and Converting 19 Reference 23 3 Output 25 3.1 Tree Format 26 3.2 Numeric Formats 29 3.2.1 Default Format 29 3.2.2 Defined Format 31 3.3 Extended Formats 32 3.3.1 Rounding 32 3.3.2 Parts of Coefficients 33 3.4 Selected Components 35 3.5 Primitive Formats 36 3.6 Recovered Values 38 4 Unary Operations 41 4.1 Theory 41 4.1.1 Negation 41 4.1.2 Involution 41 4.1.3 Pair Exchange 42 4.1.4 Reversion 43 4.1.5 Clifford Conjugation 44 4.1.6 Supplementation and Pseudo-scalar 44 4.2 Practice 45 4.2.1 Example Code 45 4.2.2 Example Output 47 5 Binary Operations 49 5.1 Geometric Origins 49 5.1.1 Outer Multiplication 49 5.1.2 Orthogonal Components 52 5.1.3 Inner Multiplication 53 5.1.4 Names 54 5.2 Multiplication of Units 55 5.2.1 Progressive and Regressive Multiplication 55 5.2.2 Outer, Inner, and Central Multiplication 57 5.2.3 Multiplication By Scalars 58 5.3 Central Multiplication 59 5.3.1 Primal Units 60 5.3.2 Evolved and Other Units 61 5.3.3 Numbers 62 5.4 Practice 63 5.4.1 Example Code 63 5.4.2 Example Output 65 5.4.3 Multiplication Tables 65 References 70 6 Vectors and Geometry 71 6.1 Theory 71 6.1.1 Magnitude 71 6.1.2 Inverse 72 6.1.3 Reflection 72 6.1.4 Projection 73 6.1.5 Rotation 73 6.2 Practice 74 6.2.1 Example Code 74 6.2.2 Example Output 76 7 Quaternions 79 7.1 Theory 79 7.1.1 Magnitude 80 7.1.2 Inverse 80 7.1.3 Reflection and Projection 80 7.1.4 Rotation 81 7.1.5 Intersection 82 7.1.6 Factorisation 82 7.2 Practice 83 7.2.1 Example Code 83 7.2.2 Example Output 86 References 87 8 Pauli Matrices 89 8.1 Theory 89 8.1.1 Recovery of Components 90 8.1.2 Magnitude 90 8.1.3 Inverse 91 8.1.4 Reflection, Projection, and Rotation 91 8.2 Practice 91 8.2.1 Example Code 91 8.2.2 Example Output 94 Reference 95 9 Bicomplex Numbers 97 9.1 Theory 97 9.1.1 Conjugate 98 9.1.2 Magnitude 98 9.1.3 Inverse 98 9.1.4 Reflection, Projection, and Rotation 99 9.2 Practice 99 9.2.1 Example Code 99 9.2.2 Example Output 101 Reference 102 10 Electromagnetic Fields 103 10.1 Theory 103 10.1.1 Time and Frequency 103 10.1.2 Electromagnetic Entities 104 10.1.3 Dirac Operators 105 10.1.4 Maxwell’s Equations 105 10.1.5 Simplified Notation 105 10.1.6 Magnitude 106 10.1.7 Inverse 106 10.1.8 Reflection 107 10.1.9 Projection 107 10.1.10 Rotation 107 10.2 Practice 107 10.2.1 Example Code 107 10.2.2 Example Output 110 10.3 Field Arithmetic 112 10.3.1 Extensions Based on Quaternions 112 10.3.2 Inverses 113 10.3.3 Example Code 115 10.3.4 Example Output 117 References 118 11 Arrays of Clifford Numbers 119 11.1 Theory 119 11.2 Practice 120 11.2.1 Example Code 120 11.2.2 Example Output 123 Reference 125 12 Power Series 127 12.1 Theory 127 12.1.1 User Defined 127 12.1.2 Predefined 128 12.1.3 Convergence 129 12.1.4 Factorisation 130 12.1.5 Squaring 131 12.2 Practice 131 12.2.1 User Defined 131 12.2.2 Predefined 133 12.2.2.1 Standard Convergence 136 12.2.2.2 Extended Convergence 141 12.2.2.3 Doubly Extended Convergence 146 References 148 13 Matrices of Clifford Numbers 149 13.1 Background 149 13.2 Inversion 150 13.3 Practice 152 13.3.1 Example Code 152 13.3.2 Example Output 155 Reference 159 Part II Customisation 161 14 Memory 163 14.1 Memory Usage 163 14.2 Examples 165 14.2.1 Memory Tree Sparsity 165 14.2.2 Memory Expansion 170 14.2.3 Memory Recycling 171 14.2.3.1 Explicit and Implicit 171 14.2.3.2 Implicit and Nested 173 Reference 175 15 Errors 177 15.1 User Errors 177 15.1.1 Syntax Errors and Messages 180 15.2 System Errors 181 15.3 Recovery 182 15.4 Beneficial Usage 185 Reference 191 16 Extension 193 16.1 Accumulation 193 16.2 Multiplication 195 16.3 Transformation 197 16.4 Filtration 198 Part III Application 203 17 Verification 205 17.1 Identities 205 17.2 Tests 205 17.2.1 Example Code 205 17.2.2 Example Output 208 Reference 214 18 Lines Not Parallel 215 18.1 Theory 215 18.1.1 Common Plane 215 18.1.1.1 Inner Product 216 18.1.1.2 Outer Product 217 18.1.1.3 Geometrical Interpretation 217 18.1.2 No Plane in Common 218 18.1.2.1 Inner Product 219 18.1.2.2 Solution 219 18.2 Practice 220 18.2.1 Example Code 220 18.2.2 Example Output 223 Reference 224 19 Perspective Projection 225 19.1 Theory 225 19.2 Practice 225 19.2.1 Example Code 225 19.2.2 Example Output 229 Reference 230 20 Linear Systems 231 20.1 Theory 231 20.2 Practice 233 20.2.1 Example Code 233 20.2.2 Example Output 235 References 235 21 Fast Fourier Transform 237 21.1 Theory 237 21.2 Practice 238 21.2.1 Example Code 238 21.2.2 Example Output 243 References 244 22 Hertzian Dipole 245 22.1 Theory 245 22.2 Practice 246 22.2.1 Example Code 246 22.2.2 Example Output 251 Reference 253 23 Finite Difference Time Domain 255 23.1 Theory 255 23.1.1 Analytical Solution 255 23.1.2 Series Solution 256 23.1.3 Analytical Example 257 23.1.4 Numerical Derivatives 257 23.2 Practice 259 23.2.1 Example Code 259 23.2.2 Example Output 265 References 270 24 Cauchy Extension 271 24.1 Background 271 24.2 Theory 272 24.2.1 Two Dimensions 272 24.2.2 Three Dimensions 272 24.2.3 Singularity 273 24.2.4 The Taming Function 273 24.2.5 Construction 274 24.3 Practice 276 24.3.1 Example Code 276 24.3.2 Example Output 281 References 284 25 Electromagnetic Scattering 285 25.1 Background 285 25.2 Theory 286 25.3 Practice 288 25.3.1 Example Code 288 25.3.2 Example Output 289 References 293 Part IV Programming 295 26 Interfaces 297 26.1 Configuration and Observation 297 26.1.1 Management 297 26.1.2 Printing 298 26.2 Simple Entities 300 26.2.1 Units 300 26.2.2 Components 300 26.2.3 Numbers 302 26.2.3.1 Establishing and Recovering Values 302 26.2.3.2 Functions 303 26.2.3.3 Addition and Subtraction 304 26.2.3.4 Multiplication 304 26.2.3.5 Geometric 305 26.2.3.6 Filtering 305 26.3 Higher Entities 306 26.3.1 Vectors 306 26.3.2 Bicomplex Numbers 307 26.3.3 Quaternions 307 26.3.4 Pauli Matrices 308 26.3.5 Electromagnetic Fields 308 26.4 Multiple Entities 309 26.4.1 Arrays 309 26.4.2 Fast Fourier Transforms 309 26.4.3 Series 310 26.4.4 Matrices 310 Reference 311 27 Descriptions 313 27.1 Arguments 313 27.2 Data types 313 27.3 Formats 315 27.4 Manual Pages 316 27.4.1 A–e 316 27.4.2 F–j 342 27.4.3 K–o 369 27.4.4 P–t 387 27.4.5 U–z 468 27.5 Quick Reference 477 Reference 487 A Key to Example Code and Results 489 Index 493
£85.50
Springer NonEquilibrium Entropy and Irreversibility Mathematical Physics Studies 5
Book Synopsis1. Introduction and Summary.- 2. Dynamics and Work.- 3. Information Entropy.- 3.a Entropy and relative entropy.- 3.b Gibbs states.- 3.c Entropy-increasing processes.- 4. Heat Baths.- 5. Reversible Processes.- 6. Closed Finite Systems.- 6.a Available work.- 6.b Recurrences.- 6.c Entropy functions.- 7. Open Systems.- 7.a Markov description.- 7.b Available work and entropy.- 7.c Master equation models.- 8. External Perturbations.- 8.a Models of the perturbations.- 8.b Classical systems.- 8.c Quantum systems.- 8.d Effects on the entropy functions.- 9. Thermodynamic Limit.- 10. Thermodynamic Entropy.- 10.a Thermodynamic processes and entropy.- 10.b Properties of the entropy functions.- 10.c Irreversibility and approach to equilibrium.- 11. Measurements, Entropy and Work.- 11.a Observations on the system.- 11.b Information and entropy.- 11.c Exchange of work and heat.- 12. Other Approaches.- Appendix A. Quantum Markov Processes.- A.1 Reduced dynamics.- A.2 Markov processes.- A.3 Non-passivitTable of Contents1. Introduction and Summary.- 2. Dynamics and Work.- 3. Information Entropy.- 3.a Entropy and relative entropy.- 3.b Gibbs states.- 3.c Entropy-increasing processes.- 4. Heat Baths.- 5. Reversible Processes.- 6. Closed Finite Systems.- 6.a Available work.- 6.b Recurrences.- 6.c Entropy functions.- 7. Open Systems.- 7.a Markov description.- 7.b Available work and entropy.- 7.c Master equation models.- 8. External Perturbations.- 8.a Models of the perturbations.- 8.b Classical systems.- 8.c Quantum systems.- 8.d Effects on the entropy functions.- 9. Thermodynamic Limit.- 10. Thermodynamic Entropy.- 10.a Thermodynamic processes and entropy.- 10.b Properties of the entropy functions.- 10.c Irreversibility and approach to equilibrium.- 11. Measurements, Entropy and Work.- 11.a Observations on the system.- 11.b Information and entropy.- 11.c Exchange of work and heat.- 12. Other Approaches.- Appendix A. Quantum Markov Processes.- A.1 Reduced dynamics.- A.2 Markov processes.- A.3 Non-passivity of Markov processes.- A.4 Non-KMS property of Markov processes.- A.5 Quantum thermal fluctuations.- Appendix B. Sensitivity of Hyperbolic Motion.- References.- Notation Index.
£94.99
Springer-Verlag New York Inc. Hilbert Space Operators in Quantum Physics
Book SynopsisThe new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.Trade ReviewFrom the reviews of the second edition: Some praise for the previous edition: “I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....” (John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder) "This is an excellent textbook for graduate students and young researchers in mathematics and theoretical physics. … It is a course from the basics in functional analysis to bounded and unbounded operators, including spectral theory and operator algebras. The exposition is comprehensive, but self-contained." (Michael Demuth, Zentralblatt MATH, Vol. 1163, 2009) “As the title declares, the text presents a comprehensive presentation of linear spaces and their transformations. … this second edition contains two additional chapters on quantum treatments of waveguides and graphs. … The book considered is, no doubt, written for physicists and useful for them. … A valuable feature of this book is the extensive background material and discussions collected into separate sections. … The book does what it promises and does it well.” (Stig Stenholm, Contemporary Physics, January, 2010)Table of ContentsPreface to the second edition, Preface,. 1.Some notions from functional analysis,Vector and normed spaces,1.2 Metric and topological spaces,1.3 Compactness, 1.4 Topological vector spaces, 1.5 Banach spaces and operators on them, 1.6 The principle of uniform boundedness, 1.7 Spectra of closed linear operators, Notes to Chapter 1, Problems 2. Hilbert spaces, 2.1 The geometry of Hilbert spaces, 2.2 Examples, 2.3 Direct sums of Hilbert spaces, 2.4 Tensor products, 2.4 Notes to Chapter 2, Problems 3. Bounded operators, 3.1 Basic notions, 3.2 Hermitean operators, 3.3 Unitary and isometric operators, 3.4 Spectra of bounded normal operators, 3.5 Compact operators, 3.6 Hilbert-Schmidt and trace-class operators, Notes to Chapter 3, Problems 4. Unbounded operators, 4.1 The adjoint, 4.2 Closed operators, 4.3 Normal operators. Self-adjointness, 4.4 Reducibility. Unitary equivalence, 4.5 Tensor products, 4.6 Quadratic forms, 4.7 Self-adjoint extensions, 4.8 Ordinary differential operators, 4.9 Self-adjoint extensions of differential operators, Notes to Chapter 4, Problems 5. Spectral Theory , 5.1 Projection-valued measures, 5.2 Functional calculus, 5.3 The spectral Tudorem, 5.4 Spectra of self-adjoint operators, 5.5 Functions of self-adjoint operators, 5.6 Analytic vectors, 5.7 Tensor products, 5.8 Spectral representation, 5.9 Groups of unitary operators, Notes to Chapter 5, Problems 6. Operator sets and algebra, 6.1 C^*-algebras, 6.2 GNS construction, 6.3 W^*-algebras, 6.4 Normal states on W^*-algebras, 6.5 Commutative symmetric operator sets, 6.6 Complete sets of commuting operators, 6.7 Irreducibility. Functions of non-commuting operators, 6.8 Algebras of unbounded operators, Notes to Chapter 6, Problems 7. States and observables, 7.1 Basic postulates, 7.2 Simple examples, 7.3 Mixed states, 7.4 Superselection rules, 7.5 Compatibility, 7.6 The algebraic approach, Notes to Chapter 7, Problems 8. Position and momentum, 8.1 Uncertainty relations, 8.2 The canonical commutation relations, 8.3 The classical limit and quantization, Notes to Chapter 8, Problems 9. Time evolution, 9.1 The fundamental postulate, 9.2 Pictures of motion, 9.3 Two examples, 9.4 The Feynman integral, 9.5 Nonconservative systems, 9.6 Unstable systéme, Notes to Chapter 9, Problems 10. Symmetries of quantum systéme, 10.1 Basic notions, 10.2 Some examples, 10.3 General space-time transformations, Notes to Chapter 10, Problems 11. Composite systems, 11.1 States and observables, 11.2 Reduced states, 11.3 Time evolution, 11.4 Identical particles, 11.5 Separation of variables. Symmetries, Notes to Chapter 11, Problems 12. The second quantization, 12.1 Fock spaces, 12.2 Creation and annihilation operators, 12.3 Systems of noninteracting particles, Notes to Chapter 12, Problems 13. Axiomatization of quantum theory, 13.1 Lattices of propositions, 13.2 States on proposition systems, 13.3 Axioms for quantum field theory, Notes to Chapter 13, Problems 14. Schrödinger operators, 14.1 Self-adjointness, 14.2 The minimax principle. Analytic perturbations, 14.3 The discrete spectrum, 14.4 The essential spectrum, 14.5 Constrained motion, 14.6 Point and contact interactions, Notes to Chapter 14, Problem 15. Scattering theory, 15.1 Basic notions ,15.2 Existence of wave operators, 15.3 Potential scattering, 15.4 A model of two-channel scattering, Notes to Chapter 15, Problems 16. Quantum waveguides, 16.1 Geometric effects in Dirichlet stripes, 16.2 Point
£98.99
Johns Hopkins University Press Tensor Calculus for Physics
Book SynopsisIt is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.Trade ReviewThis book is well written and has sufficient rigor to allow students to use it for independent study. Choice An introductory Tensor Calculus for Physics book is a most welcome addition... Professor Neuenschwander's book fills the gap in robust fashion. American Journal of PhysicsTable of ContentsPrefaceAcknowledgmentsChapter 1. Tensors Need Context1.1. Why Aren't Tensors Defined by What They Are?1.2. Euclidean Vectors, without Coordinates1.3. Derivatives of Euclidean Vectors with Respect to a Scalar1.4. The Euclidean Gradient1.5. Euclidean Vectors, with Coordinates1.6. Euclidean Vector Operations with and without Coordinates1.7. Transformation Coefficients as Partial Derivatives1.8. What Is a Theory of Relativity?1.9. Vectors Represented as Matrices1.10. Discussion Questions and ExercisesChapter 2. Two-Index Tensors2.1. The Electric Susceptibility Tensor2.2. The Inertia Tensor2.3. The Electric Quadrupole Tensor2.4. The Electromagnetic Stress Tensor2.5. Transformations of Two-Index Tensors2.6. Finding Eigenvectors and Eigenvalues2.7. Two-Index Tensor Components as Products of Vector Components2.8. More Than Two Indices2.9. Integration Measures and Tensor Densities2.10. Discussion Questions and ExercisesChapter 3. The Metric Tensor3.1. The Distinction between Distance and Coordinate Displacement3.2. Relative Motion3.3. Upper and Lower Indices3.4. Converting between Vectors and Duals3.5. Contravariant, Covariant, and "Ordinary" Vectors3.6. Tensor Algebra3.7. Tensor Densities Revisited3.8. Discussion Questions and ExercisesChapter 4. Derivatives of Tensors4.1. Signs of Trouble4.2. The Affine Connection4.3. The Newtonian Limit4.4. Transformation of the Affine Connection4.5. The Covariant Derivative4.6. Relation of the Affine Connection to the Metric Tensor4.7. Divergence, Curl, and Laplacian with Covariant Derivatives4.8. Disccussion Questions and ExercisesChapter 5. Curvature5.1. What Is Curvature?5.2. The Riemann Tensor5.3. Measuring Curvature5.4. Linearity in the Second Derivative5.5. Discussion Questions and ExercisesChapter 6. Covariance Applications6.1. Covariant Electrodynamics6.2. General Covariance and Gravitation6.3. Discussion Questions and ExercisesChapter 7. Tensors and Manifolds7.1. Tangent Spaces, Charts, and Manifolds7.2. Metrics on Manifolds and Their Tangent Spaces7.3. Dual Basis Vectors7.4. Derivatives of Basis Vectors and the Affine Connection7.5. Discussion Questions and ExercisesChapter 8. Getting Acquainted with Differential Forms8.1. Tensors as Multilinear Forms8.2. 1-Forms and Their Extensions8.3. Exterior Products and Differential Forms8.4. The Exterior Derivative8.5. An Application to Physics: Maxwell's Equations8.6. Integrals of Differential Forms8.7. Discussion Questions and ExercisesAppendix A: Common Coordinate SystemsAppendix B: Theorem of AlternativesAppendix C: Abstract Vector SpacesBibliographyIndex
£37.05
Simon & Schuster Models Behaving Badly Why Confusing Illusion with
Book Synopsis
£14.39
Springer-Verlag New York Inc. Practical Bifurcation and Stability Analysis
Book SynopsisFifteen years have elapsed after the second edition of Practical Bifurcation and Stability Analysis was published. Along with the high level of sophistication that bifurcation analysis has reached, the research on basic computational bifurcation algorithms is essentially completed, at least in - dinary di?erential equations.Trade ReviewFrom the reviews of the third edition:"The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society“Methods of practical bifurcation and stability analysis are crucial instruments in applied mathematics. This fact stimulated the author to publish an up-to-date third edition, sixteen years after appearing the second edition. … The references contain more than 600 items. The excellent presentation of the material will stimulate people in applied sciences to apply the well-prepared instruments.” (Klaus R. Schneider, Zentralblatt MATH, Vol. 1195, 2010)Table of Contentsand Prerequisites.- Basic Nonlinear Phenomena.- Applications and Extensions.- Principles of Continuation.- Calculation of the Branching Behavior of Nonlinear Equations.- Calculating Branching Behavior of Boundary-Value Problems.- Stability of Periodic Solutions.- Qualitative Instruments.- Chaos.
£89.99
Springer-Verlag New York Inc. Introduction to Applied Nonlinear Dynamical
Book SynopsisThis introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: Will serve as one of the most eminent introductions to the geometric theory of dynamical systems. --Monatshefte für MathematikTrade ReviewFrom the reviews of the second edition:"This is a very substantial revision of the author’s original textbook published in 1990. It does not only contain much new material, for instance on invariant manifold theory and normal forms, it has also been restructured. … The presentation is intended for advanced undergraduates … . This second edition … will serve as one of the most eminent introductions to the geometric theory of dynamical systems." (R. Bürger, Monatshefte für Mathematik, Vol. 145 (4), 2005)"This is an extensively rewritten version of the first edition which appeared in 1990, taking into account the many changes in the subject during the intervening time period. … The book is suitable for use as a textbook for graduate courses in applied mathematics or cognate fields. It is written in a readable style, with considerable motivation and many insightful examples. … Overall, the book provides a very accessible, up-to-date and comprehensive introduction to applied dynamical systems." (P.E. Kloeden, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 85 (1), 2005)"The second edition of this popular text … is an encyclopedic introduction to dynamical systems theory and applications that includes substantial revisions and new material. It should be on the reading list of every student of the subject … . Also, the new organization makes the book more suitable as a textbook that can be used in graduate courses. This book will also be a useful reference for applied scientists … as well as a guide to the literature." (Carmen Chicone, Mathematical Reviews, 2004h)"This volume includes a significant amount of new material. … Each chapter starts with a narrative … and ends with a large collection of excellent exercises. … An extensive bibliography … provide a useful guide for future study. … This is a highly recommended book for advanced undergraduate and first-year graduate students. It contains most of the necessary mathematical tools … to apply the results of the subject to problems in the physical and engineering sciences." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 75, 2009)“It is certainly one of the most complete introductory textbooks about dynamical systems, though no single book can be really complete. … Some chapters can certainly be used as a course text for a master’s course, but the whole book is to thick for a single course. … a suitable first text for Ph.D. students who want to do research in dynamical systems, and a useful reference work for more experienced people. I definitely enjoyed reading this book and can only recommend it.” (Kurt Lust, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)Table of ContentsEquilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index Theory * Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows * Asymptotic Behavior * The Poincaré-Bendixson Theorem * Poincaré Maps * Conjugacies of Maps, and Varying the Cross-Section * Structural Stability, Genericity, and Transversality * Lagrange's Equations * Hamiltonian Vector Fields * Gradient Vector Fields * Reversible Dynamical Systems * Asymptotically Autonomous Vector Fields * Center Manifolds * Normal Forms * Bifurcation of Fixed Points of Vector Fields * Bifurcations of Fixed Points of Maps * On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution * The Smale Horseshoe * Symbolic Dynamics * The Conley-Moser Conditions or 'How to Prove That a Dynamical System is Chaotic' * Dynamics Near Homoclinic Points of Two-Dimensional Maps * Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields * Melnikov's Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields * Liapunov Exponents * Chaos and Strange Attractors * Hyperbolic Invariant Sets: A Chaotic Saddle * Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems * Global Bifurcations Arising from Local Codimension-Two Bifurcations * Glossary of Frequently Used Terms
£67.49
Springer New York Quantum Field Theory
Book SynopsisTrade ReviewFrom the reviews: "The monograph is composed on the basis of courses on field theory and particle physics which have been taught by the author … . Besides exposition of the basic topics in quantum field theory (QFT) it illustrates also various applications of the methods … . The discussion of each topic given in the present book is accompanied by references … . The book will be useful for those students and researchers who are familiar with non-relativistic quantum mechanics and wish to have acquaintance with QFT." (Michael B. Mensky, Zentralblatt MATH, Vol. 1077, 2006) "This book is an interesting item in the list of textbooks on quantum field theory. Contrary to many disciplines of theoretical physics there is still no widely accepted canonical set of such textbooks. The present book is a good candidate to enter such a list. Firstly, it has two advantages: it is modern and relatively compact. Also, the clarity and economy of this text are evident … . The compactness of the book is achieved through the way topics are presented … ." (Andrzej M. Frydryszak, Mathematical Reviews, Issue 2006 d)Table of ContentsResults in Relativistic Quantum Mechanics.- The Construction of Fields.- Canonical Quantization.- Commutators and Propagators.- Interactions and the S-matrix.- The Electromagnetic Field.- Examples of Scattering Processes.- Functional Integral Representations.- Renormalization.- Gauge Theories.- Symmetry.- Spontaneous symmetry breaking.- Anomalies I.- Elements of differential geometry.- Path Integrals.- The Configuration Space in Nonabelian Gauge Theory.- Anomalies II.- Finite temperature and density.- Gauge theory: Nonperturbative questions.- Elements of Geometric Quantization.
£67.49
Springer New York Nodal Discontinuous Galerkin Methods Algorithms Analysis and Applications 54 Texts in Applied Mathematics
Book SynopsisThis book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.Trade ReviewFrom the reviews: "This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering." -Mathematical Reviews "The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k) "This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008)Table of ContentsThe key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension.
£62.99
Springer New York Mathematical Methods of Classical Mechanics 60 Graduate Texts in Mathematics
Book SynopsisI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem.- Appendix 9 Poincaré's geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.Trade ReviewSecond Edition V.I. Arnol’d Mathematical Methods of Classical Mechanics "The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." —AMERICAN MATHEMATICAL MONTHLYTable of ContentsI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov’s theorem.- Appendix 9 Poincaré’s geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.
£52.24
Springer-Verlag New York Inc. Advanced Mathematical Methods for Scientists and
Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index
£49.49
Springer New York Geometry Particles and Fields Graduate Texts in Contemporary Physics
Book SynopsisI. Basic Properties of Particles and Fields.- 1. Electromagnetism.- 2. Interaction of Fields and Particles.- 3. Dynamics of Classical Fields.- 4. Solitons.- 5. Path Integrals and Instantons.- II. Basic Principles and Applications of Differential Geometry.- 6. Differentiable Manifolds?Tensor Analysis.- 7. Differential Forms and the Exterior Calculus.- 8. Integral Calculus on Manifolds.- 9. Dirac Monopoles.- 10. Smooth Maps?Winding Numbers.- 11. Symmetries and Conservation Laws.Trade ReviewFROM THE REVIEWS: MATHEMATICAL REVIEWS"It is particularly well-suited as an introductory text, since the author takes great care to anticipate points that may cause confusion…The author does a good job of focusing on the fundamentals…[The first] part of the book works as either a self-contained introduction to classical field theory, or as a complement to a good text on classical electrodynamics…[The second] part of the book is very clear and well planned…works as a self-contained introduction to manifolds and differential forms, or, even better, as a compliment to a concise mathematics text.” PHYSICS TODAY"The present volume is a welcome edition to the growing number of books that develop geometrical language and use it to describe new developments in particle physics ... It provides clear treatment that is accessible to graduate students with a knowledge of advanced calculus and of classical physics.... The second half of the book deals with the principles of differential geometry and its applications, with a mathematical machinery of very wide range. Here clear line drawings and illustrations supplement the multitude of mathematical definitions. This section, in its clarity and pedagogy, is reminiscent of Gravitation by Charles Misner, Kip Thorne and John Wheeler.... Felsager gives a very clear presentation of the use of geometric methods in particle physics.... For those who have resisted learning this new language, his book provides a very good introduction as well as physical motivation. The inclusion of numerous exercises, worked out, renders the book useful for independent study also. I hope this book will be followed by others from authors with equal flair to provide a readable excursion into the next step." Table of ContentsPart I: Basic Properties of Particles and Fields; 1. Electromagnetism; 2. Interaction of Fields and Particles; 3. Dynamics of Classical Fields; 4. Solitons; 5. Path-Integrals and Instantons; Part II: Basic Principles and Applications of Differential Geometry; 6. Differentiable Manifolds-Tensor Analysis; 7. Differential Forms and the Exterior Algebra; 8. Integral Calculus on Manifolds; 9. Dirac Monopoles; 10. Smooth Maps-Winding Numbers; 11. Symmetries and Conservation Laws
£75.99
Springer New York Multiple Scale and Singular Perturbation Methods 114 Applied Mathematical Sciences
Book Synopsis1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit Process Expansions for Ordinary Differential Equations.- 2.1. The Linear Oscillator.- 2.2. Linear Singular Perturbation Problems with Variable Coefficients.- 2.3. Model Nonlinear Example for Singular Perturbations.- 2.4. Singular Boundary Problems.- 2.5. Higher-Order Example: Beam String.- References.- 3. Limit Process Expansions for Partial Differential Equations.- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations.- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow.- 3.3. Singular Boundary Problems.- References.- 4. The Method of Multiple Scales for Ordinary Differential Equations.- 4.1. Method of Strained Coordinates for Periodic Solutions.- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator.- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators.- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators.- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form.- References.- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance.- 5.1. General Systems in Standard Form: Nonresonant Solutions.- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions.- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance.- 5.4. Prescribed Frequency Variations, Transient Resonance.- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance.- References.- 6. Multiple-Scale Expansions for Partial Differential Equations.- 6.1. Nearly Periodic Waves.- 6.2. Weakly Nonlinear Conservation Laws.- 6.3. Multiple-Scale Homogenization.- References.Table of Contents1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit Process Expansions for Ordinary Differential Equations.- 2.1. The Linear Oscillator.- 2.2. Linear Singular Perturbation Problems with Variable Coefficients.- 2.3. Model Nonlinear Example for Singular Perturbations.- 2.4. Singular Boundary Problems.- 2.5. Higher-Order Example: Beam String.- References.- 3. Limit Process Expansions for Partial Differential Equations.- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations.- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow.- 3.3. Singular Boundary Problems.- References.- 4. The Method of Multiple Scales for Ordinary Differential Equations.- 4.1. Method of Strained Coordinates for Periodic Solutions.- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator.- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators.- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators.- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form.- References.- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance.- 5.1. General Systems in Standard Form: Nonresonant Solutions.- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions.- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance.- 5.4. Prescribed Frequency Variations, Transient Resonance.- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance.- References.- 6. Multiple-Scale Expansions for Partial Differential Equations.- 6.1. Nearly Periodic Waves.- 6.2. Weakly Nonlinear Conservation Laws.- 6.3. Multiple-Scale Homogenization.- References.
£143.99
Springer New York The Evolution of Dynamics Vibration Theory from 1687 to 1742 Vibration Theory from 1687 to 1742 Vibration Theory from 1687 to 1742 Studies in the History of Mathematics and Physical Sciences
Book SynopsisIn this study we are concerned with Vibration Theory and the Problem of Dynamics during the half century that followed the publication of Newton's Principia. In fact, it was through problems posed by Vibration Theory that a general theory of Dynamics was motivated and discovered.Table of Contents1. Introduction.- 2. Newton (1687).- 2.1. Pressure Wave.- 2.2. Remarks.- 3. Taylor (1713).- 3.1. Vibrating String.- 3.2. Absolute Frequency.- 3.3. Remarks.- 4. Sauveur (1713).- 4.1. Vibrating String.- 4.2. Remarks.- 5. Hermann (1716).- 5.1. Pressure Wave.- 5.2. Vibrating String.- 5.3. Remarks.- 6. Cramer (1722).- 6.1. Sound.- 6.2. Remarks.- 7. Euler (1727).- 7.1. Vibrating Ring.- 7.2. Sound.- 8. Johann Bernoulli (1728).- 8.1. Vibrating String (Continuous and Discrete).- 8.2. Remark on the Energy Method.- 9. Daniel Bernoulli (1733; 1734); Euler (1736) …..- 9.1. Linked Pendulum and Hanging Chain.- 9.2. Laguerre Polynomials and J0.- 9.3. Double and Triple Pendula.- 9.4. Roots of Polynomials.- 9.5. Zeros of J0.- 9.6. Other Boundary Conditions.- 9.7. The Bessel Functions Jv.- 10. Euler (1735).- 10.1. Pendulum Condition.- 10.2. Vibrating Rod.- 10.3. Remarks.- 11. Johann II Bernoulli (1736).- 11.1. Pressure Wave.- 11.2. Remarks.- 12. Daniel Bernoulli (1739; 1740).- 12.1. Floating Body.- 12.2. Remarks.- 12.3. Dangling Rod.- 12.4. Remarks on Superposition.- 13. Daniel Bernoulli (1742).- 13.1. Vibrating Rod.- 13.2. Absolute Frequency and Experiments.- 13.3. Superposition.- 14. Euler (1742).- 14.1. Linked Compound Pendulum.- 14.2. Dangling Rod and Weighted Chain.- 15. Johann Bernoulli (1742) no.- 15.1. One Degree of Freedom.- 15.2. Dangling Rod.- 15.3. Linked Pendulum I.- 15.4. Linked Pendulum II.- Appendix: Daniel Bernoulli’s Papers on the Hanging Chain and the Linked Pendulum.- Theoremata de Oscillationibus Corporum.- De Oscillationibus Filo Flexili Connexorum.- Theorems on the Oscillations of Bodies.- On the Oscillations of Bodies Connected by a Flexible Thread.
£58.49
Birkhauser Boston Inc Linear Integral Equations
Book SynopsisMany physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.Trade ReviewA nice introductory text... Presents the basics of linear integral equations theory in a very comprehensive way... [The] richness of examples and applications makes the book extremely useful for teachers and also researchers. —Applications of Mathematics (Review of the Second Edition) This second edition of this highly useful book continues the emphasis on applications and presents a variety of techniques with extensive examples...The book is ideal as a text for a beginning graduate course. Its excellent treatment of boundary value problems and an up-to-date bibliography make the book equally useful for researchers in many applied fields.—MathSciNet (Review of the Second Edition)Table of ContentsIntroduction.- Integral Equations with Separable Kernels.- Method Of Successive Approximations.- Classical Fredholm Theory.- Applications of Ordinary Differential Equations.- Applications of Partial Differential Equations.- Symmetric Kernels.- Singular Integral Equations.- Integral Transformation Methods.- Applications to Mixed Boundary Value Problems.- Integral Equations Perturbation Methods.- Appendix.- Bibliography.- Index.
£49.49
Taylor & Francis Inc Handbook of Ordinary Differential Equations
Book SynopsisThe Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available.Table of ContentsEXACT SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS: First-Order Differential Equations. Second-Order Differential Equations. Third-Order Differential Equations. Fourth-Order Differential Equations. Higher-Order Differential Equations. Systems of Ordinary Differential Equations. SOLVING METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: First-Order Differential Equations. Second-Order Linear Differential Equations. Second-Order Nonlinear Differential Equations. Linear Equations of Arbitrary Order. Nonlinear Equations of Arbitrary Order. Analytic Ordinary Differential Equations and Their Local Classification. Lie Group and Discrete Group Methods. Linear Systems of Ordinary Differential Equations. Nonlinear Systems of Ordinary Differential Equations. Integrability of Polynomial Differential Systems. Hamiltonian Systems, Periodic, and Homoclinic Solutions by Variational Methods. Bifurcation Theory of Limit Cycle of Planar Systems. Successive Approximation Method for Nonlinear Boundary Value Problems. Application of Integral Equations for the Investigation of Differential Equations. Exact Methods for Construction of Particular Solutions for Nonlinear Equations. SYMBOLIC AND NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH MAPLE, MATHEMATICA, AND MATLAB: Ordinary Differential Equations with Maple. Ordinary Differential Equations with Mathematica. Ordinary Differential Equations with MATLAB. Supplements. References. Index.
£266.00
MP-NCA Uni of North Carolina Differential Geometry in Physics
Book Synopsis
£20.76
MP-AMM American Mathematical Random Matrices and the SixVertex Model
Book Synopsis
£103.50
