Integral Equations and Their Applications
Title | Integral Equations and Their Applications PDF eBook |
Author | Matiur Rahman |
Publisher | WIT Press |
Pages | 385 |
Release | 2007 |
Genre | Mathematics |
ISBN | 1845641019 |
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.
Singular Integral Equations
Title | Singular Integral Equations PDF eBook |
Author | N. I. Muskhelishvili |
Publisher | Courier Corporation |
Pages | 466 |
Release | 2013-02-19 |
Genre | Mathematics |
ISBN | 0486145069 |
DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div
Hypersingular Integral Equations and Their Applications
Title | Hypersingular Integral Equations and Their Applications PDF eBook |
Author | I.K. Lifanov |
Publisher | CRC Press |
Pages | 416 |
Release | 2003-12-29 |
Genre | Mathematics |
ISBN | 0203402162 |
A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co
Singular Differential and Integral Equations with Applications
Title | Singular Differential and Integral Equations with Applications PDF eBook |
Author | R.P. Agarwal |
Publisher | Springer Science & Business Media |
Pages | 412 |
Release | 2013-06-29 |
Genre | Mathematics |
ISBN | 9401730040 |
In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.
Linear and Nonlinear Integral Equations
Title | Linear and Nonlinear Integral Equations PDF eBook |
Author | Abdul-Majid Wazwaz |
Publisher | Springer Science & Business Media |
Pages | 639 |
Release | 2011-11-24 |
Genre | Mathematics |
ISBN | 3642214495 |
Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
Linear Integral Equations
Title | Linear Integral Equations PDF eBook |
Author | William Vernon Lovitt |
Publisher | |
Pages | 280 |
Release | 1924 |
Genre | Integral equations |
ISBN |
Lectures on Functional Equations and Their Applications
Title | Lectures on Functional Equations and Their Applications PDF eBook |
Author | J. Aczel |
Publisher | Courier Corporation |
Pages | 548 |
Release | 2006-02-01 |
Genre | Mathematics |
ISBN | 0486445232 |
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.