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

The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics.

David Porter (Author), David S. G. Stirling (Author)

9780521337427, Cambridge University Press

Paperback, published 28 September 1990

388 pages
22.8 x 15.2 x 2.3 cm, 0.548 kg

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

This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems. The book 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 which arise in application areas. Since it is not always possible to find explicit solutions of the problems posed, much attention is devoted to obtaining qualitative information and approximations to the solutions, with the associated error estimates. This treatment is intended for final year mathematics undergraduates, postgraduates and research workers in application areas such as numerical analysis and fluid mechanics.

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.

Subject Areas: Calculus & mathematical analysis [PBK]