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Bulletin of the American Mathematical Society Volume 20

Bulletin of the American Mathematical Society Volume 20


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914 edition. Excerpt: ...an order a 1 for x = is then discussed. Finally the case when K(x, x) = 0 is considered. In discussing this case the elegant method of Lalesco, which consists in making use of linear differential equations, is applied. The author next considers systems of integral equations and equations containing multiple integrals and shows how the ordinary methods can without serious complications be extended to these cases. A few pages are then devoted to the method of successive approximations as applied to integral equations. Other topics of which a brief discussion is given are generalized equations of the Volterra type, equations where the two limits of integration are variable, and non-linear equations. In Chapter III equations of the Fredholm type V(x) = U(x) +-k k(x, are discussed. The same method of considering the given equation as the limiting case of a system of algebraic equations is used in treating this type. The kernel is supposed to be finite. The case where the kernel becomes infinite is discussed very briefly. A few pages are devoted to systems of equations and equations involving multiple integrals. At the end of the chapter some very interesting applications are made to Dirichlet's problem and to the vibration of strings. In Chapter IV a very brief and incomplete account of integro-differential equations is given. By such an equation is meant one involving not only the unknown functions under signs of integration but also the unknown functions themselves and their derivatives. No attempt is made to give a systematic treatment of this subject. A few problems from mechanics leading to equations of this kind are discussed. A few pages are also devoted to permutable functions. For a more complete discussion of these very...


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Product Details
  • ISBN-13: 9781130673135
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 206
  • Spine Width: 11 mm
  • Width: 189 mm
  • ISBN-10: 1130673138
  • Publisher Date: 13 Sep 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 376 gr


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