Integral Equations: A Practical Treatment, from Spectral Theory to Applications

ISBN-13: 9780521337427 / Angielski / Miękka / 1990 / 388 str.

David Porter; David S. Stirling; D. G. Crighton

Opis

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.

Recenzje

"...an excellent way to gain acquaintance with integral equations... Jet Wimp, The Mathematical Intelligencer

Spis treści

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.