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Books > Science & Mathematics > Mathematics > Applied mathematics
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Singular Integral Equations (Paperback, Softcover reprint of the original 1st ed. 2000)
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Singular Integral Equations (Paperback, Softcover reprint of the original 1st ed. 2000)
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Many physical problems that are usually solved by differential
equation techniques can be solved more effectively by integral
equation methods. This work focuses exclusively on singular
integral equations and on the distributional solutions of these
equations. A large number of beautiful mathematical concepts are
required to find such solutions, which in tum, can be applied to a
wide variety of scientific fields - potential theory, me chanics,
fluid dynamics, scattering of acoustic, electromagnetic and earth
quake waves, statistics, and population dynamics, to cite just
several. An integral equation is said to be singular if the kernel
is singular within the range of integration, or if one or both
limits of integration are infinite. The singular integral equations
that we have studied extensively in this book are of the following
type. In these equations f (x) is a given function and g(y) is the
unknown function. 1. The Abel equation x x) = l g (y) d 0 < a
< 1. ( / Ct y, ( ) a X - Y 2. The Cauchy type integral equation
b g (y) g(x)=/(x)+).. l--dy, a y-x where).. is a parameter. x
Preface 3. The extension b g (y) a (x) g (x) = J (x) +).. l--dy , a
y-x of the Cauchy equation. This is called the Carle man equation.
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