The Solution of Certain Integral Equations With Kernels K(z, (Zeta))/(Z-(Zeta)) (Classic Reprint) - Couverture souple

A. S. Peters

Couverture souple

ISBN 10 : 1332972276 ISBN 13 : 9781332972272

Editeur : Forgotten Books, 2018

Synopsis

Master the methods for solving integral equations with singular kernels and boundary value insights. This book presents a practical approach to equations with kernels that have simple poles, guiding you from standard procedures to extended techniques. It blends classical ideas with new twists to help you see how complex analysis connects to integral equations.

The discussion starts with a clear setup of the problem and assumptions, then develops a pathway from the integral equation to a Hilbert-Riemann boundary value problem. Along the way, you’ll learn how to handle principal values, factor F(w), and manage indices and zeros that affect solvability. The text also shows how to derive existence conditions and how these conditions translate into concrete equations you can solve.

- Understand the standard method and the extended techniques for equations with singular kernel parts
- See how Cauchy principal values and boundary values relate to analytic constructions
- Learn to formulate existence conditions and reduce problems to linear systems
- Explore special cases and how different kernel choices affect solutions

Ideal for readers of advanced calculus and applied mathematics who want a solid, methodical approach to integral equations and their analytical underpinnings. This edition is well suited for students and professionals seeking a rigorous path from problem setup to explicit solutions.

A propos du livre

Présentation de l'éditeur

I ntroduction. It is well known that the solution of the integral equation (z) ffzj =h(?) (?) +m) can be reduced to the Hilbert-xliernann boundary value problem which is defined inS ection 2. This reduction, which depends on the ideas of Carleman and Plemelj, is explained in detail in the texts by II uskhelishvili [1], Gahov [2], and others; and it is now regarded as a standard method. It is the purpose of this paper to show that a moi eelementary method can be used to solve various types of integral equations involving Cauchy kernels provided certain conditions are satisfied. The function theoretic method described below avoids the analysis of aH ilbert-P aemann boundary value problem; consequently, when it can be used, it is more simple and rapid than the standard procedure. Furthermore, it can be used to solve some equations to which the standard method is inapplicable. The method described inS ection 3involves the Plemelj formulas and little more than the theory of residues. It is of such an elementary nature that one would expect to find it in a place of some prominence in the texts, or surmise at least that it appears elsewhere. However, a more or less intensive search of the literature failed to reveal any reference to it. This led the author to believe that a presentation of it in this report might be useful.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text.

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1332972276
• ISBN 13: 9781332972272
• Reliure: Broché
• Nombre de pages: 87
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