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Integral Equations

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Handbook of Applied Mathematics

Abstract

An integral equation is a functional equation in which the unknown variable ø appears under an integral sign. In the case of a single independent variable x, a form commonly encountered can be written as

$$g(x)\phi (x)=f(x)+\lambda \int_{a}^{b}{F[x,\xi ;\phi (\xi )]}d\xi \text{ }(a\le x\le b)$$
(10.1-1)

In this expression, f (x) and g(x) are known functions, and ø(x) is to be determined. The form of the functional F is known, λ is a parameter, and the range of integration [a, b] is specified.

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References

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Author information

Authors and Affiliations

  1. Dep’ts. of Oceanography and Applied Mathematics, University of Washington, Seattle, Wash., 98195, USA

    Prof. Donald F. Winter

Authors
  1. Prof. Donald F. Winter
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Editor information

Editors and Affiliations

  1. University of Washington, USA

    Carl E. Pearson (Professor of Applied Mathematics) (Professor of Applied Mathematics)

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© 1990 Van Nostrand Reinhold

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Winter, D.F. (1990). Integral Equations. In: Pearson, C.E. (eds) Handbook of Applied Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1423-3_10

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  • DOI: https://doi.org/10.1007/978-1-4684-1423-3_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-442-00521-4

  • Online ISBN: 978-1-4684-1423-3

  • eBook Packages: Springer Book Archive

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