Lectures on Differential and Integral Equations

by Kosaku Yosida

Dover, 1991, 0486666794, Trade Paperback, VG condition, top corner bump on spine, no underlining, no highlighting, 220 pages.

 

 

This is a lucid, self-contained exposition of the theory of ordinary differential equations and integral equations. Written for advanced undergraduates and graduate students, the book gives an especially detailed treatment of the boundary value problem of second order linear ordinary differential equations, and includes an elementary exposition of the theory of Weyl-Stone's eigenfunction expansions in the form completed by Titchmarsh-Kodaira's formula concerning the density matrix of the expansion.

Unabridged Dover (1991) republication of the edition published by Interscience Publishers, New York, 1960. Foreword. Bibliography. Index. ix + 220pp. 5-3/8 x 8-1/2. Paperbound.

 


CONTENTS


I. The Initial Value Problem for Ordinary Differential Equations (Successive Approximations, Linear Differential Equations of the nth Order, Second Order Differential Equations of the Fuchs Type)


II. The Boundary Value Problem for Linear Differential Equations of Second Order (Boundary Value Problem, Hilbert-Schmidt Theory of Integral Equations with Symmetric Kernels, Asymptotic Expression of Eigenvalues and Eigenfunctions, Liouville's Method)


III. Fredholm Integral Equations (Fredholm Alternative Theorem, Schmidt Expansion Theorem and the Mercer Expansion Theorem, Singular Integral Equations)


IV. Volterra Integral Equations (Volterra Integral Equations of the Second Kind, Volterra Integral Equations of the First Kind)


V. The General Expansion Theorem (Weyl-Stone-Titchmarsh-Kodaira's Theorem)

(Classification of Singular Boundary Points, General Expansion Theorem, Examples)


VI. Non-Linear Integral Equations

Appendix (From the Theory of Functions of a Complex Variable)