Sturm-Liouville Problems: Theory and Numerical Implementation (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) - Hardcover

Guenther, Ronald B.; Lee, John W

Hardcover

ISBN 10: 1138345431 ISBN 13: 9781138345430

Publisher: CRC Press, 2018

Synopsis

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified 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.

About this title

About the Author

Ronald B. Guenther is an Emeritus Professor in the Department of Mathematics at Oregon State University. His research interests include 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.

Review

This is a mathematically rigorous, comprehensive, self-contained treatment of the elegant Sturm-Liouville theory. The book sets the stage with a review of classical applications involving buckling, vibrations, heat conduction and calculus of variations.

The role of Green's functions is introduced. In order to make the discussion which follows self-contained, a relevant review of real analysis is presented. Although experienced readers could skip this part, it is pleasing to see how nicely such results are frequently used to present the theory and carry out the proofs of the theorems.

Chapters are presented on integral equations, operators and kernels, regular and singular Sturm-Liouville problems. A thorough treatment is given on oscillation, approximation and orthogonality of eigenfunctions for regular and singular problems. Interlacement results for the zeros of eigenfunctions are given.

While classical examples leading to Bessel functions, Legendre polynomials, etc. are described, it must be admitted that closed formulae for solutions are seldom available for arbitrary systems and therefore a chapter is dedicated to numerical methods for approximating solutions. For this purpose, a chapter is dedicated to the description of the shooting method for differential equations, and numerical examples are presented. Combining the numerical discussion with the excellent analysis discussion makes the book unique. The book is rounded out with a relevant bibliography.

-Gene Allgower, Colorado State University

Sturm-Liouville theory is part of the bedrock of classical applied mathematics and mathematical physics. Guenther and Lee provide a excellently motivated compendium of topics ranging from physical considerations (Euler buckling, vibrations, diffusion, etc.) to integral representations and equations, the role of function spaces for solutions, and the Sturm-Liouville systems themselves. Graduate and advanced undergraduate students in applied mathematics and the physical sciences will find the development natural and leisurely, balancing mathematical rigor with intuition. A pleasant read.

-John Crow, Blackbird Analytics LLC

Edition details

• Publisher: CRC Press
• Publication date: 2018
• ISBN 10: 1138345431
• ISBN 13: 9781138345430
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 420