45: Integral equations
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.
Browse all (old) classifications for this area at the AMS.
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