Singular Integral Equations - Softcover

Estrada, Ricardo; Kanwal, Ram P.

Softcover

ISBN 10: 1461271231 ISBN 13: 9781461271239

Verlag: Birkhäuser, 2012

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 1461271231
• ISBN 13: 9781461271239
• Einband: Taschenbuch
• Anzahl der Seiten: 444
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