Green's Functions and Boundary Value Problems by Ivar Stakgold (Wiley, 1979) HC

This updated version of a popular applied math book reflects the changes in the field and includes new material on modeling and nonlinear analysis as well as additional exercises and problems.

A Systematic analysis of boundary value problems and the principal methods used for their solution, including those based on Green's functions and eigenfunction expansions. Provides necessary background in functional analysis through the study of distributions, Hilbert spaces, integral equations, and spectral theory. Reviews of metric spaces and contraction mappings, spectral theory, transforms, and partial differential equations progress to a treatment of nonlinear problems, including bifurcation and monotone methods. Special sections provide careful derivations of equations in chemical reaction engineering; emphasis on dependence on the data overview of Green's function; a unified treatment of delta sequences; Riesz Schauder theory; and continuous spectrum. Also discusses modeling and approximation techniques such as perturbation theory and variational methods. Examples are chosen from a wide range of applications in engineering and physical sciences.