Sturm-Liouville Theory

2005 Education

Author : Anton Zettl
Release : 2005
Genre : Education
Kind : eBook
Book Rating : 671/5 ( reviews)

Book Synopsis Sturm-Liouville Theory by : Anton Zettl

Download or read book Sturm-Liouville Theory written by Anton Zettl. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.

Sturm-Liouville Theory and its Applications

2008-01-15 Mathematics

Author : Mohammed Al-Gwaiz
Release : 2008-01-15
Genre : Mathematics
Kind : eBook
Book Rating : 718/5 ( reviews)

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Book Synopsis Sturm-Liouville Theory and its Applications by : Mohammed Al-Gwaiz

Download or read book Sturm-Liouville Theory and its Applications written by Mohammed Al-Gwaiz. This book was released on 2008-01-15. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.

Sturm-Liouville Theory

2005-12-05 Mathematics

Author : Werner O. Amrein
Release : 2005-12-05
Genre : Mathematics
Kind : eBook
Book Rating : 598/5 ( reviews)

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Book Synopsis Sturm-Liouville Theory by : Werner O. Amrein

Download or read book Sturm-Liouville Theory written by Werner O. Amrein. This book was released on 2005-12-05. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Theory of a Higher-Order Sturm-Liouville Equation

2006-11-13 Mathematics

Author : Vladimir Kozlov
Release : 2006-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 227/5 ( reviews)

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Book Synopsis Theory of a Higher-Order Sturm-Liouville Equation by : Vladimir Kozlov

Download or read book Theory of a Higher-Order Sturm-Liouville Equation written by Vladimir Kozlov. This book was released on 2006-11-13. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Multiparameter Eigenvalue Problems

2010-12-07 Mathematics

Author : F.V. Atkinson
Release : 2010-12-07
Genre : Mathematics
Kind : eBook
Book Rating : 239/5 ( reviews)

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Book Synopsis Multiparameter Eigenvalue Problems by : F.V. Atkinson

Download or read book Multiparameter Eigenvalue Problems written by F.V. Atkinson. This book was released on 2010-12-07. Available in PDF, EPUB and Kindle. Book excerpt: One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem

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Sturm-Liouville Theory

Sturm-Liouville Theory and its Applications

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