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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.