The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation. Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results Contents selected and organized to suit the needs of students, scientists, and engineers Contains tables of Laplace and Fourier transform pairs New section on numerical approximation New section on the z-transform Easy reference system
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener–Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. With 300 additional pages, this edition covers much more material than its predecessor. New to the Second Edition • New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions • More than 400 new equations with exact solutions • New chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs • Additional examples for illustrative purposes To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations.
Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.
The Table of Integrals, Series, and Products is the major reference source for integrals in the English language.It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems. *Completely reset edition of Gradshteyn and Ryzhik reference book *New entries and sections kept in orginal numbering system with an expanded bibliography *Enlargement of material on orthogonal polynomials, theta functions, Laplace and Fourier transform pairs and much more.
Author: Chapman & Hall/CRC Taylor & Francis Group, LLC
PREFACE TO THE NEW EDITION Handbook of Integral Equations, Second Edition, a unique reference for engineers and scientists, contains over 2,500 integral equationswith solutions, aswell as analytical and numerical methods for solving linear and nonlinear equations. It considersVolterra,Fredholm,Wiener–Hopf,Hammerstein, Urysohn, and other equations,which arise inmathematics, physics, engineering sciences, economics, etc. In total, the number of equations described is an order of magnitude greater than in any other book available. The second edition has been substantially updated, revised, and extended. It includes new chapters on mixed multidimensional equations, methods of integral equations for ODEs and PDEs, and about 400 new equations with exact solutions. It presents a considerable amount of new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions. Many examples were added for illustrative purposes. The new edition has been increased by a total of over 300 pages. Note that the first part of the book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations. We would like to express our deep gratitude to Alexei Zhurov and Vasilii Silvestrov for fruitful discussions. We also appreciate the help of Grigory Yosifian in translating new sections of this book and valuable remarks. The authors hope that the handbookwill prove helpful for a wide audience of researchers, college and university teachers, engineers, and students in various fields of appliedmathematics, mechanics, physics, chemistry, biology, economics, and engineering sciences. A. D. Polyanin A. V. Manzhirov Andrei D. Polyanin, D.Sc., Ph.D., is a well-known scientist of broad interests and is active in various areas of mathematics, mechanics, and chemical engineering sciences. He is one of the most prominent authors in the field of reference literature on mathematics and physics. Professor Polyanin graduated with honors from the Department of Mechanics and Mathematics of Moscow State University in 1974. He received his Ph.D. degree in 1981 and D.Sc. degree in 1986 at the Institute for Problems inMechanics of the Russian (former USSR) Academy of Sciences. Since 1975, Professor Polyanin has been working at the Institute for Problems in Mechanics of the Russian Academy of Sciences; he is also Professor of Mathematics at Bauman Moscow State Technical University. He is a member of the Russian National Committee on Theoretical and Applied Mechanics and of the Mathematics and Mechanics Expert Council of the Higher Certification Committee of the Russian Federation. Professor Polyanin has made important contributions to exact and approximate analytical methods in the theory of differential equations, mathematical physics, integral equations, engineering mathematics, theory of heat and mass transfer, and chemical hydrodynamics. He obtained exact solutions for several thousand ordinary differential, partial differential, and integral equations. Professor Polyanin is an author of more than 30 books in English, Russian, German, and Bulgarian as well as over 120 research papers and three patents. He has written a number of fundamental handbooks, including A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, 1995 and 2003; A. D. Polyanin and A. V.Manzhirov, Handbook of Integral Equations, CRC Press, 1998; A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, 2002; A. D. Polyanin, V. F. Zaitsev, and A. Moussiaux, Handbook of First Order Partial Differential Equations, Taylor & Francis, 2002; A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, 2004, and A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2007. Professor Polyanin is editor of the book series Differential and Integral Equations and Their Applications, Chapman & Hall/CRC Press, London/Boca Raton, and Physical and Mathematical Reference Literature, Fizmatlit, Moscow. He is also Editor-in-Chief of the international scientificeducational Website EqWorld—The World of Mathematical Equations (http://eqworld.ipmnet.ru), which is visited by over 1700 users a dayworldwide. Professor Polyanin is a member of the Editorial Board of the journal Theoretical Foundations of Chemical Engineering. In 1991, Professor Polyaninwas awarded a Chaplygin Prize of the Russian Academy of Sciences for his research in mechanics. In 2001, he received an award from the Ministry of Education of the Russian Federation. Address: Institute for Problems in Mechanics, Vernadsky Ave. 101 Bldg 1, 119526 Moscow, Russia Home page: http://eqworld.ipmnet.ru/polyanin-ew.htm Alexander V. Manzhirov, D.Sc., Ph.D., is a noted scientist in the fields of mechanics and applied mathematics, integral equations, and their applications. After graduating with honors from the Department of Mechanics and Mathematics of Rostov State University in 1979, Alexander Manzhirov attended postgraduate courses at Moscow Institute of Civil Engineering. He received his Ph.D. degree in 1983 at Moscow Institute of Electronic Engineering Industry and D.Sc. degree in 1993 at the Institute for Problems in Mechanics of the Russian (former USSR) Academy of Sciences. Since 1983, Alexander Manzhirov has been working at the Institute for Problems in Mechanics of the Russian Academy of Sciences. Currently, he is head of the Laboratory for Modeling in Solid Mechanics at the same institute. Professor Manzhirov is also head of a branch of the Department of Applied Mathematics at Bauman Moscow State Technical University, professor of mathematics at Moscow State University of Engineering andComputer Science, vice-chairman of Mathematics and Mechanics ExpertCouncil of the Higher Certification Committee of the Russian Federation, executive secretary of Solid Mechanics Scientific Council of the Russian Academy of Sciences, and expert in mathematics, mechanics, and computer science of the Russian Foundation for Basic Research. He is a member of theRussian NationalCommittee on Theoretical and AppliedMechanics and the European Mechanics Society (EUROMECH), and member of the editorial board of the journal Mechanics of Solids and the international scientific-educational Website EqWorld—The World of Mathematical Equations (http://eqworld.ipmnet.ru). ProfessorManzhirov has made important contributions to newmathematical methods for solving problems in the fields of integral equations and their applications, mechanics of growing solids, contact mechanics, tribology, viscoelasticity, and creep theory. He is an author of more than ten books (including Contact Problems in Mechanics of Growing Solids [in Russian], Nauka, Moscow, 1991; Handbook of Integral Equations,CRC Press, Boca Raton, 1998;Handbuch der Integralgleichungen: Exacte L¨osungen, Spektrum Akad. Verlag, Heidelberg, 1999; Contact Problems in the Theory of Creep [in Russian], National Academy of Sciences of Armenia, Erevan, 1999; A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2007), more than 70 research papers, and two patents. Professor Manzhirov is a winner of the First Competition of the Science Support Foundation 2001, Moscow. Address: Institute for Problems in Mechanics, Vernadsky Ave. 101 Bldg 1, 119526 Moscow, Russia. Home page: http://eqworld.ipmnet.ru/en/board/manzhirov.htm.
Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.
A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.
Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately, there's Schaum's. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you More than 2,400 formulas and tables Covers elementary to advanced math topics Arranged by topics for easy reference Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
This handbook presents many known results as well as new classes of integrals, series, power expansions, and productions of elementary and special functions. It shows how modern computer algebra methods are used to solve various problems in science and engineering. The second volume of the set contains formulas devoted to mathematical physics, including the Meijer G-function and properties of hypergeometric functions. Using these tools, readers can evaluate and simplify numerous new integrals and sums.
The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source. Over 10, 000 mathematical entries Most up to date listing of integrals, series and products (special functions) Provides accuracy and efficiency in industry work 25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend to approximately 35% of new updates
Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung
Author: Julian Havil
Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.