This book addresses in a unifed way the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.

Ronald B. Guenther is an Emeritus Professor in the Department of Mathematics at Oregon State University. His research interests include fluid mechanics and mathematically modelling deterministic systems and the ordinary and partial differential equations that arise from these models.

John W. Lee is an Emeritus Professor in the Department of Mathematics at Oregon State University. His research interests include differential equations, especially oscillatory properties of problems of Sturm-Liouville type and related approximation theory, and integral equations.

Preface. 1 Setting the Stage. 2 Preliminaries. 3 Integral Equations. 4 Regular Sturm-Liouville Problems. 5 Singular Sturm-Liouville Problems - I. 6 Singular Sturm-Liouville Problems - II. 7 Approximation of Eigenvalues and Eigenfunctions. 8 Concluding Examples and Observations. A Mildly Singular Compound Kernels. B Iteration of Mildly Singular Kernels. C The Kellogg Conditions