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

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

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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.
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"...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 subjects involved." A. Corduneanu, Mathematical Reviews "...this is not a treatise but an excellent book from which to learn the subject, and therefore at least as valuable for the undergraduate library. Its level is just right for the beginning graduate student or the highly motivated senior." Choice "...a very good book for students who want to become familiar with the basic theory of linear integral equations." Harry Hochstadt, SIAM Review " excellent way to gain acquaintance with integral equations... Jet Wimp, The Mathematical Intelligencer
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Table of contents

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.
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