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Author: Harry Hochstadt
Publisher: John Wiley & Sons
ISBN: 1118165934
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.
Author: Harry Hochstadt
Publisher: John Wiley & Sons
ISBN: 1118165934
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.
Author: Dr Jitendra Singh
Publisher: Dr. Jitendra Singh
ISBN:
Category : Education
Languages : en
Pages : 138
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Book Description
This book is part of the P-17 series designed specifically for the CSIR NET (JRF) in Mathematical Sciences and other competitive mathematics examinations. Integral equations play a crucial role in various fields, including applied mathematics, physics, and engineering. This text aims to provide a comprehensive introduction to integral equations, offering both theoretical insights and practical problem-solving techniques. Chapter 1 lays the groundwork by differentiating between Fredholm and Volterra integral equations and clarifying the distinctions between first- and second-kind integral equations. Understanding these foundational concepts is essential for tackling more complex topics. In Chapter 2, we explore several methods for solving integral equations, including the resolvent kernel method and the Neumann series approach. These techniques provide powerful tools for both analytical and numerical solutions. Chapter 3 delves into separable kernels, showcasing their significance in solving integral equations and their applications in mathematical physics and engineering contexts. Chapter 4 addresses eigenvalue problems, connecting characteristic numbers and eigenfunctions to the well-established Sturm-Liouville theory, which is pivotal in understanding the spectral properties of differential operators. Finally, Chapter 5 discusses the resolvent kernel, detailing its theory and applications in solving integral equations effectively. This book aims to equip students and researchers with the knowledge and skills necessary to navigate the complexities of integral equations, fostering a deeper appreciation for their applications in both pure and applied mathematics.
Author: Nicolaï Saltykow
Publisher: FeniXX
ISBN: 2706239670
Category : Science
Languages : fr
Pages : 82
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Book Description
Cet ouvrage est une réédition numérique d’un livre paru au XXe siècle, désormais indisponible dans son format d’origine.
Author: Ram P. Kanwal
Publisher: Academic Press
ISBN: 1483262502
Category : Mathematics
Languages : en
Pages : 311
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Book Description
Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.
Author: Wolfgang Hackbusch
Publisher: Birkhäuser
ISBN: 3034892152
Category : Mathematics
Languages : en
Pages : 377
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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: Matiur Rahman
Publisher: WIT Press
ISBN: 1845641019
Category : Mathematics
Languages : en
Pages : 385
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Book Description
The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Author: Tofigh Allahviranloo
Publisher: Springer Nature
ISBN: 3030853500
Category : Technology & Engineering
Languages : en
Pages : 222
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Book Description
This book suggests that the numerical analysis subjects’ matter are the important tools of the book topic, because numerical errors and methods have important roles in solving integral equations. Therefore, all needed topics including a brief description of interpolation are explained in the book. The integral equations have many applications in the engineering, medical, and economic sciences, so the present book contains new and useful materials about interval computations including interval interpolations that are going to be used in interval integral equations. The concepts of integral equations are going to be discussed in two directions, analytical concepts, and numerical solutions which both are necessary for these kinds of dynamic systems. The differences between this book with the others are a full discussion of error topics and also using interval interpolations concepts to obtain interval integral equations. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit the subjects of the book.
Author: Mario Paul Ahues
Publisher: Springer Science & Business Media
ISBN: 0817681841
Category : Mathematics
Languages : en
Pages : 296
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Book Description
* Good reference text; clusters well with other Birkhauser integral equations & integral methods books (Estrada and Kanwal, Kythe/Puri, Constanda, et al). * Includes many practical applications/techniques for applied mathematicians, physicists, engineers, grad students. * The contributors to the volume draw from a number of physical domains and propose diverse treatments for various mathematical models through the use of integration as an essential solution tool. * Physically meaningful problems in areas related to finite and boundary element techniques, conservation laws, hybrid approaches, ordinary and partial differential equations, and vortex methods are explored in a rigorous, accessible manner. * The new results provided are a good starting point for future exploitation of the interdisciplinary potential of integration as a unifying methodology for the investigation of mathematical models.
Author: M. A. Goldberg
Publisher: Springer Science & Business Media
ISBN: 1475714661
Category : Science
Languages : en
Pages : 351
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Book Description
Author: Traian Lalescu
Publisher:
ISBN:
Category : Integral equations
Languages : fr
Pages : 172
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Book Description
