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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 45: Integral equations

Introduction

Integral equations, naturally, seek functions which satisfy relationships with their integrals. For example, the value of a function at each time may be related to its average value over all preceding time. Included in this area are equations mixing integration and differentiation. Many of the themes from differential equations recur: qualitative questions, methods of approximation, specific types of equations of interest, transforms and operators useful for simplifying the problems.

History

Applications and related fields

Subfields

• 45A05: Linear integral equations
• 45B05: Fredholm integral equations
• 45C05: Eigenvalue problems, See also 34LXX, 35PXX, 45P05, 47A75
• 45D05: Volterra integral equations, See also 34A12
• 45E: Singular integral equations, see also 30EXX, 44-XX, 30E20, 30E25, 44A15, 44A35
• 45F: Systems of linear integral equations
• 45G: Nonlinear integral equations, see also 47H15
• 45H05: Miscellaneous special kernels, See also 44A15
• 45J05: Integro-ordinary differential equations
• 45K05: Integro-partial differential equations
• 45M: Qualitative behavior
• 45N05: Abstract integral equations, integral equations in abstract spaces
• 45P05: Integral operators, See also 47B38, 47G10
• 45Q05: Inverse problems [new in 2000]
• 45R05: Random integral equations (See also 60H20) [new in 2000]

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Wing, G. Milton: "A primer on integral equations of the first kind. The problem of deconvolution and unfolding", Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1991. 135 pp. ISBN 0-89871-263-7 MR93d:45001

Jörgens, Konrad: "Linear integral operators", Surveys and Reference Works in Mathematics, 7. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. 379 pp. ISBN 0-273-08523-9 MR83j:45001

Software and tables

Other web sites with this focus

• Here are the AMS and Goettingen resource pages for area 45.

Selected topics at this site

• Example of homogeneous Fredholm integral equation
• Numerical solution of Fredholm integral equations of the first kind