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**About this book :- **
**Linear Integral Equations ** written by
** William Vernon Lovitt**.

This book is an English edition of Japanese book by Iwanami Shoten in the series "Iwanami Zensho". Its is exposition of the theory of ordinary differential equaitons and integral equations. It is especially gives detailed treatement of the boundary value problem of second order linear ordinary differenital equations and elementry exposition of Weyl-Stone's eigenfunction expansions in the form completed by Titchmarsh Kodaira's formula concerning the density matrix expansion.

Lucid, self-contained exposition of the theory of ordinary differential equations and integral equations. Especially detailed treatment of the boundary value problem of second order linear ordinary differential equations. Other topics include Fredholm integral equations, Volterra integral equations, much more. Bibliography.

**Book Detail :- **
** Title: ** Linear Integral Equations
** Edition: **
** Author(s): ** William Vernon Lovitt
** Publisher: ** Dover Publications
** Series: ** Dover Phoenix Editions
** Year: ** 2005
** Pages: ** 279
** Type: ** PDF
** Language: ** English
** ISBN: ** 9780486442853,0486442853
** Country: ** US

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**About Author :- **

The Author Kosaku Yosida Professor of Mathematics, Colorada College, US.

Lovitt was born in Whiting, Kansas, and earned his bachelor's degree from the University of Nebraska. After graduate work at the University of Chicago, Lovitt taught at the University of Nebraska, the University of Washington, Harvard University, and Purdue University before arriving in Colorado Springs. Lovitt and Sisam arrived the same year (1918) to take the place of Florian Cajori.

Lovitt lived somewhat in the shadow of Charles Sisam who was the head of the department (they apparently never spoke), but in the middle of his long career at Colorado College, US, he became the Dean of Men (1928-1938). Views were mixed on his effectiveness; one of the college historians, Juan Reid, refers to his "arbitrary decisions in disciplinary matters." He attracted considerable student opprobrium through his dismissal of two editors of The Tiger (the CC student newspaper).

He maintained an active scholarly life publishing many papers and five books:

• Mathematics for Students of Agriculture and General Science - Kenyon and Lovitt (1918)

• Linear Integral Equations - Lovitt (1924)

• The Mathematics of Business - Lovitt and Holtzclow (1926)

• Statistics - Lovitt and Holtzclow (1929)

• Elementary Theory of Equations (1939)

Lovitt became chair of the mathematics department briefly when Sisam left in 1948. After retiring from the college, he moved to San Mateo, California where he died in 1972.

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**Book Contents :- **
**Linear Integral Equations** written by
** William Vernon Lovitt **
cover the following topics.

1. Introduction

2. Solution of Integral Equation of Second Kind by Successive Substitutions

3. Solution of Fredholm's Equation Expressed as Ratio of two Integral Series in lemda

4. Application of the Fredhom Theory

i) Free Vibration of an Elastic String

ii) Constrained Vibrations of an Elastic String

iii) Auxiliary Theorems on Harmonic Functions

iv) Logarithmic Potential of 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

5. Hilbert-Schmidt Theory of Integral Equations with Symmetric Kernels

i) Existence of at Least one Characteristic Constant

ii) Orthogonality

iii) Equation of Arithmetic Function

iv) Expansion of Kernel according to the Fundamental Functions of a complete Normalized Orthogonal System

v) Auxiliary Theorems

vi) Solution of Integral Equations

6. Application of the Hilbert Schmidt Theory

i) Boundary Problems for Ordinary Linear Differential Equations

ii) Applications to the Second Variation

iii) Vibration Problems

iv) Applications of the Hilbert Schmidt Theory to the Flow of Heat in a Bar

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