Integral Equations

This classic work is now available in an unabridged paperback edition. Hochstatdt′s concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.

Partial table of contents: BASIC EXISTENCE THEOREMS. Fixed Point Theorems. Volterra Equations. Kernels with Weak Singularities. INTEGRAL EQUATIONS WITH L2 KERNELS. Compact Operators. Positive Operators. Approximation of Eigenvalues. Fredholm Equations with Self–Adjoint Compact Operators. APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS. FOURIER TRANSFORMS. Laplace Transforms. Hankel Transforms. Mellin Transforms. The Weiner–Hopf Technique I. The Weiner–Hopf Technique II. THE FREDHOLM THEORY. NONLINEAR INTEGRAL EQUATIONS. The Schauder Fixed Point Theorem. Index.