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Handbook of integral equations. 2nd ed. (English) Zbl 1154.45001
Boca Raton, FL: CRC Press (ISBN 978-1-58488-507-8/hbk). xxxii, 1108 p. (2008).
This well-known handbook is now a standard reference. It contains over 2,500 integral equations with solutions, as well as analytical and numerical methods for solving linear and nonlinear equations. It considers Volterra, Fredholm, Wiener-Hopf, Hammerstein, Urysohn, and other equations, which arise in mathematics, 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 ordinary and partial differential equations, 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.
More information on the contents may be obtained from the review of the Russian original (2003; Zbl 1021.45001), the German translation (1999; Zbl 0916.45001), and the first English edition (1998; Zbl 0896.45001).

MSC:
45-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations
00A22 Formularies
65R20 Numerical methods for integral equations
45Exx Singular integral equations
65Rxx Numerical methods for integral equations, integral transforms
45Gxx Nonlinear integral equations
45L05 Theoretical approximation of solutions to integral equations
45P05 Integral operators
45D05 Volterra integral equations
44-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms
33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions
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