Author: I. G. Petrovskii
Publisher: Courier Corporation
ISBN: 9780486697567
Category : Mathematics
Languages : en
Pages : 142
Get Book Here
Book Description
Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Author: Ivan Georgievich Petrovski
Publisher:
ISBN:
Category : Integral equations
Languages : en
Pages : 97
Get Book Here
Book Description
Author: Ivan Georgievič Petrovskij
Publisher:
ISBN:
Category :
Languages : en
Pages : 135
Get Book Here
Book Description
Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486817822
Category : Mathematics
Languages : en
Pages : 145
Get Book Here
Book Description
Concise classic presents main results of integral equation theory as consequences of theory of operators on Banach and Hilbert spaces. Also, applications to second order linear differential equations and Fourier integral techniques. 1969 edition.
Author: K?saku Yoshida
Publisher: Courier Corporation
ISBN: 9780486666792
Category : Mathematics
Languages : en
Pages : 242
Get Book Here
Book Description
Lucid, self-contained exposition of theory of ordinary differential equations and integral equations. Boundary value problem of second order linear ordinary differential equations, Fredholm integral equations, many other topics. Bibliography. 1960 edition.
Author: Wolfgang Hackbusch
Publisher: Birkhäuser
ISBN: 3034892152
Category : Mathematics
Languages : en
Pages : 377
Get Book Here
Book Description
The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Author: John Wiedhofft Gough
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Weng Cho Chew
Publisher: Morgan & Claypool Publishers
ISBN: 1598291483
Category : Elastic waves
Languages : en
Pages : 259
Get Book Here
Book Description
Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Author: Ivan Georgievich Petrovskiĭ
Publisher:
ISBN:
Category : Integral equations
Languages : en
Pages :
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Integral equations
Languages : ru
Pages : 120
Get Book Here
Book Description
