Integral equations : a practical treatment from spectral theory to applications / David Porter, David S. G. Stirling

This book contains the following chapters: (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 selfadjoint operator, (6) Positive operators, (7) Approximation methods for eigenvalues and eigenvectors of selfadjoint operators, (8) Approximation methods for inhomogeneous integral equations, (9) Some singular integral equations.
Every chapter ends with a representative list of proposed exercises and problems; the book contains about two hundred such questions. Some examples are completely solved in the text. It is assumed that the reader knows the classical mathematical analysis, linear algebra and elementary notions from the theory of differential equations. The theory of linear operators in Hilbert spaces is rigorously presented and then used to obtain classical results for the Fredholm integral equations. In particular, we note the spectral theory of compact selfadjoint operators and its applications. The authors pay special attention to the conversion of the problems of differential equations with initial or boundary conditions into integral equations. Besides many classical problems in this theory, the final chapters of the book contain some results which seem to be new. 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. (MathSciNet)

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