Linear Integral Equations

by William Vernon Lovitt

Overview

Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics. Topics include the solution of Fredholm’s equation expressed as a ratio of two integral series in lambda, free and constrained vibrations of an elastic string, and auxiliary theorems on harmonic functions. Discussion of the Hilbert-Schmidt theory covers boundary problems for ordinary linear differential equations, vibration problems, and flow of heat in a bar. 1924 edition.

Product Details

ISBN-13:	9780486174648
Publisher:	Dover Publications
Publication date:	03/05/2014
Series:	Dover Books on Physics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	272
File size:	28 MB
Note:	This product may take a few minutes to download.

Table of Contents

I. Introductory
II. Solution of Integral Equation of Second Kind by Successive Substitutions
III. Solution of Fredholm’s Equation Expressed as Ratio of Two Integral Series in Lambda
IV. Applications of the Fredholm Theory
I. Free Vibrations of an Elastic String
II. Constrained Vibrations of an Elastic String
III. Auxiliary Theorems on Harmonic Functions
IV. Logarithmic Potential of a Double Layer
V. Fredholm’s Solution of Dirichlet’s Problem
VI. Logarithmic Potential of a Simple Layer
VII. Fredholm’s Solution of Neumann’s Problem
V. Hilbert-Schmidt Theory of Integral Equations with Symmetric Kernels
I. Existence of at Least One Characteristic Constant
II. Orthogonality
III. Expansion of an Arbitrary Function According to the fundamental functions of a Complete Normalized Orthogonal System
IV. Expansion of the Kernel According to the Fundamental Functions of a Complete Normalized Orthogonal System
V. Auxiliary Theorems
VI. Solution of the Integral Equation
VI. Applications of the Hilbert-Schmidt Theory
I. Boundary Problems for Ordinary Linear Differential Equations
II. Applications to Some Problems of the Calculus of Variations
III. Vibration Problems
IV. Applications of the Hilbert-Schmidt Theory of the Flow of Heat in a Bar
Index