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| exact form in math: Handbook of Exact Solutions to Mathematical Equations Andrei D. Polyanin, 2024-08-26 This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods. |
| exact form in math: CRC Concise Encyclopedia of Mathematics Eric W. Weisstein, 2002-12-12 Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
| exact form in math: New Methods of Celestial Mechanics Henri Poincaré, 1967 |
| exact form in math: Methods for Constructing Exact Solutions of Partial Differential Equations Sergey V. Meleshko, 2006-06-18 Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations. |
| exact form in math: Dictionary of Applied Math for Engineers and Scientists Emma Previato, 2002-10-29 Despite the seemingly close connections between mathematics and other scientific and engineering fields, practical explanations intelligible to those who are not primarily mathematicians are even more difficult to find. The Dictionary of Applied Mathematics for Engineers and Scientists fills that void. It contains authoritative yet accessible defin |
| exact form in math: Masters of Theory Andrew Warwick, 2011-04-15 Winner of the the Susan Elizabeth Abrams Prize in History of Science. When Isaac Newton published the Principia three centuries ago, only a few scholars were capable of understanding his conceptually demanding work. Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these masters of theory led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cambridge University, where many of the best physicists trained. He begins by tracing the dramatic changes in undergraduate education there since the eighteenth century, especially the gradual emergence of the private tutor as the most important teacher of mathematics. Next he explores the material culture of mathematics instruction, showing how the humble pen and paper so crucial to this study transformed everything from classroom teaching to final examinations. Balancing their intense intellectual work with strenuous physical exercise, the students themselves—known as the Wranglers—helped foster the competitive spirit that drove them in the classroom and informed the Victorian ideal of a manly student. Finally, by investigating several historical cases, such as the reception of Albert Einstein's special and general theories of relativity, Warwick shows how the production, transmission, and reception of new knowledge was profoundly shaped by the skills taught to Cambridge undergraduates. Drawing on a wealth of new archival evidence and illustrations, Masters of Theory examines the origins of a cultural tradition within which the complex world of theoretical physics was made commonplace. |
| exact form in math: Encyclopaedia of Mathematics M. Hazewinkel, 2013-12-01 |
| exact form in math: String-Math 2015 Si Li, Bong H. Lian, Wei Song, Shing-Tung Yau, 2017-11-28 This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015–January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China. Two of the main themes of this volume are frontier research on Calabi-Yau manifolds and mirror symmetry and the development of non-perturbative methods in supersymmetric gauge theories. The articles present state-of-the-art developments in these topics. String theory is a broad subject, which has profound connections with broad branches of modern mathematics. In the last decades, the prosperous interaction built upon the joint efforts from both mathematicians and physicists has given rise to marvelous deep results in supersymmetric gauge theory, topological string, M-theory and duality on the physics side, as well as in algebraic geometry, differential geometry, algebraic topology, representation theory and number theory on the mathematics side. |
| exact form in math: Spinning Strings and Correlation Functions in the AdS/CFT Correspondence Juan Miguel Nieto, 2018-07-21 This book addresses several aspects of the integrable structure of the AdS/CFT correspondence. In particular it presents computations made on both sides of the AdS/CFT correspondence, at weak and at strong coupling. On the string theory side of the correspondence, the book focuses on the evaluation of the energy spectrum of closed string solutions moving in some deformed backgrounds that preserve integrability. On the gauge theory side, it explores various formal problems arising in the computation of two and three-point functions by means of the Algebraic Bethe Ansatz and the Quantum Inverse Scattering method. The book features numerous results on integrability in the context of the AdS/CFT correspondence. Self-contained and pedagogical, it includes general discussions and detailed presentations on the use of integrable systems techniques and their applications. |
| exact form in math: A Synopsis of Elementary Results in Pure Mathematics George Shoobridge Carr, 1886 |
| exact form in math: The primordial universe - L'univers primordial P. Binetruy, 2000 This collection of conference papers reviews the link between cosmology and particle physics. It provides an introduction to supersymmetry, superstring and M-theory, whilst the contributors evaluate the cosmological consequences of these theories. |
| exact form in math: Quadratic Functions (IGCSE Math) , Confused about the various concepts on Quadratic Functions taught in school or simply want more practice questions? This book on Functions seeks to offer a condensed version of what you need to know for your journey in IGCSE Mathematics, alongside with detailed worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them. |
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| exact form in math: Maclaurin Series (A'level H2 Math) Lee Jun Cai, Confused about the various graph transformation taught in school? This book on Maclaurin Series seeks to offer a condensed version of what you need to know for A-Levels H2 Mathematics, alongside with detailed worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them. |
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| exact form in math: Encyclopaedia of Mathematics Michiel Hazewinkel, 2013-12-20 |
| exact form in math: Mathematical Reprints ... Oliver Edmunds Glenn, 1923 |
| exact form in math: Integral Equations with Difference Kernels on Finite Intervals Lev A. Sakhnovich, 2012-12-06 Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators. On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed. |
| exact form in math: Annals of Mathematics , 1923 Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics. |
| exact form in math: Hydraulics in Civil and Environmental Engineering, Fourth Edition Andrew Chadwick, John Morfett, Martin Borthwick, 2004-05-27 Find out more about Hydraulics in Civil and Environmental Engineering Fifth Edition on CRC Press at http://www.crcpress.com/product/isbn/9780415672450 |
| exact form in math: American Journal of Mathematics , 1903 The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics. |
| exact form in math: Advances in Algebraic Quantum Field Theory Romeo Brunetti, Claudio Dappiaggi, Klaus Fredenhagen, Jakob Yngvason, 2015-09-04 This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory. |
| exact form in math: International Handbook of Mathematics Education Alan Bishop, M.A. (Ken) Clements, Christine Keitel-Kreidt, Jeremy Kilpatrick, Colette Laborde, 2012-12-06 ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and practice. That documentation also reflects the fact that the field has expanded enormously in the last twenty years. At the 8th International Congress on Mathematics Education (ICME) in Seville, Spain, for example, there were 26 specialist Working Groups and 26 special ist Topic Groups, as well as a host of other group activities. In 1950 the 'Commission Internationale pour I 'Etude et l' Amelioration de l'Enseignement des Mathematiques' (CIEAEM) was formed and twenty years ago another active group, the 'International Group for the Psychology of Mathematics Education' (PME), began at the third ICME at Karlsruhe in 1976. Since then several other specialist groups have been formed, and are also active through regular conferences and publications, as documented in Edward Jacobsen's Chapter 34 in this volume. |
| exact form in math: Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory S. Pakuliak, G. von Gehlen, 2012-12-06 Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces. |
| exact form in math: From Mathematics to Philosophy (Routledge Revivals) Hao Wang, 2016-06-10 First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge. |
| exact form in math: Collected Papers II Goro Shimura, 2002-12-06 In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement : To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field. 103 of Shimura ́s most important papers are collected in four volumes. Volume II contains his mathematical papers from 1967 to 1977 and some notes to the articles. |
| exact form in math: Proceedings of the Royal Society. Section A, Mathematical and Physical Science Royal Society (Great Britain), 1928 |
| exact form in math: The One-Dimensional Hubbard Model Fabian H. L. Essler, Holger Frahm, Frank Göhmann, Andreas Klümper, Vladimir E. Korepin, 2005-02-07 This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics. |
| exact form in math: Dynamic Modeling of Environmental Systems Michael L. Deaton, James J. Winebrake, 2012-12-06 A primer on modeling concepts and applications that is specifically geared toward the environmental field. Sections on modeling terminology, the uses of models, the model-building process, and the interpretation of output provide the foundation for detailed applications. After an introduction to the basics of dynamic modeling, the book leads students through an analysis of several environmental problems, including surface-water pollution, matter-cycling disruptions, and global warming. The scientific and technical context is provided for each problem, and the methods for analyzing and designing appropriate modeling approaches is provided. While the mathematical content does not exceed the level of a first-semester calculus course, the book gives students all of the background, examples, and practice exercises needed both to use and understand environmental modeling. It is suitable for upper-level undergraduate and beginning-graduate level environmental professionals seeking an introduction to modeling in their field. |
| exact form in math: Connections Maths Ajit Kalra, James Stamell, 2004 Connections Maths 9 Stage 5. 3 / 5. 2 / 5. 1 together with Connection s Maths 10 Stage 5. 3 / 5. 2 /5. 1 provides complete coverage of the out comes for Stage 5. 3 pathway. The outcomes for theStage 5. 2 are covered in Connections Maths 9 Stage 5. 2 / 5. 1 and Connections Maths Stage 10 5. 2 / 5. 1. Features: outcomes at the start of ever y chapter a dynamic full colour design that clearly distinguish es theory, examples, exercises, and features carefully graded e xercises with worked examples and solutions linked to each cart oons offering helpful hints working mathematically strands that are fully integrated. These also feature regularly in challenging secti ons designed as extension material which also contain interesting histor ical and real life context a chapter review to revise and conso lidate learning in each chapter speed skills sections to revise and provide mental arithmetic skills problem solving applicati on strategies with communication and reasoning through an inquiry approa ch a comprehensive Diagnostic test providing a cumulative revi ew of learning in all chapters, cross referenced to each exercise integrated technology activities literacy skills develop lan guage skills relevant to each chapter fully linked icons to acc ompanying CD-ROM The student CD-ROM accompanying this text book can be used at school or at home for further explanation and learni ng. Each CD-ROM contains: interactive diagnostic tex t - perfect revision for all Stage 4 work. The regenerative nature of the program allows for an almost limitless number of varied tests of equal difficulty. This test can be used prior to commencing Stage 5 wor k dynamic geometry activities using WinGeom and Cabri software for student investigations using technology with formatted Exce l spreadsheets full textbook with links to the above |
| exact form in math: Revival: The Handbook of Software for Engineers and Scientists (1995) Paul W Ross, 2018-05-04 The Handbook of Software for Engineers and Scientists is a single-volume, ready reference for the practicing engineer and scientist in industry, government, and academia as well as the novice computer user. It provides the most up-to-date information in a variety of areas such as common platforms and operating systems, applications programs, networking, and many other problem-solving tools necessary to effectively use computers on a daily basis. Specific platforms and environments thoroughly discussed include MS-DOS®, Microsoft® WindowsTM, the Macintosh® and its various systems, UNIXTM, DEC VAXTM, IBM® mainframes, OS/2®, WindowsTM NT, and NeXTSTEPTM. Word processing, desktop publishing, spreadsheets, databases, integrated packages, computer presentation systems, groupware, and a number of useful utilities are also covered. Several extensive sections in the book are devoted to mathematical and statistical software. Information is provided on circuits and control simulation programs, finite element tools, and solid modeling tools. |
| exact form in math: Separation of Variables and Exact Solutions to Nonlinear PDEs Andrei D. Polyanin, Alexei I. Zhurov, 2021-09-19 Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training. |
| exact form in math: Encyclopaedia of Mathematics (set) Michiel Hazewinkel, 1994-02-28 The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools. |
| exact form in math: From Integrable Models to Gauge Theories S. G. Matinyan, V. G. Gurzadyan, Ara G. Sedrakian, 2002 This collection of 20 articles in honour of the noted physicist and mentor Sergei Matinyan focuses on topics that are of fundamental importance to high-energy physics, field theory and cosmology. The topics range from integrable quantum field theories, three-dimensional Ising models, parton models and tests of the Standard Model, to black holes in loop quantum gravity, the cosmological constant and magnetic fields in cosmology. A pedagogical essay by Lev Okun concentrates on the problem of fundamental units. The articles have been written by experts and are addressed to graduate students and researchers.--[Source inconnue]. |
| exact form in math: Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course Nikita Slavnov, 2022-05-12 It is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results. |
| exact form in math: Super-Recursive Algorithms Mark Burgin, 2006-12-21 * The first exposition on super-recursive algorithms, systematizing all main classes and providing an accessible, focused examination of the theory and its ramifications * Demonstrates how these algorithms are more appropriate as mathematical models for modern computers and how they present a better framework for computing methods * Develops a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole |
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