Integral Equations A Practical Treatment, from Spectral Theory to Applications [Paperback]

The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics.Blending abstract structural results and more direct, practical mathematics, this exacting study provides a thorough account of many types of integral equations, particularly in numerical analysis and fluid mechanics.Blending abstract structural results and more direct, practical mathematics, this exacting study provides a thorough account of many types of integral equations, particularly in numerical analysis and fluid mechanics.This book gives a rigorous and practical treatment of integral equations and aims to tackle the solution of integral equations using a blend of abstract structural results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text, and it allows a thorough account to be given of many of the types of integral equation that arise, particularly in numerical analysis and fluid mechanics. Because it is not always possible to find explicit solutions to the problems posed, much attention is devoted to obtaining qualitative information and approximations and the associated error estimates.Preface; 1. Classification and examples of integral equations; 2. Second order ordinary differential equations and integral equations; 3. Integral equations of the second kind; 4. Compact operators; 5. The spectrum of a compact self-adjoint operator; 6. Positive operators; 7. Approximation methods for eigenvalues and eigenvectors of self-adjoint operators; 8. Approximation methods for inhomogeneous integral equations; 9. Some singular integral equations; Appendixes; Notation index; Index. ...Porter and Stirling provide a precise and practical methodology for solving integral equations. Directions This book may be successfully used by graduate students and by any person working in the field of applied mathematics; it gives a very good treatment of all the l3Ê