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Special Functions and Generalized Sturm-Liouville Problems

2020-01-25 Mathematics
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Release : 2020-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 201/5 ( reviews)

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Book Synopsis Special Functions and Generalized Sturm-Liouville Problems by : Mohammad Masjed-Jamei

Download or read book Special Functions and Generalized Sturm-Liouville Problems written by Mohammad Masjed-Jamei. This book was released on 2020-01-25. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.

Sturm-Liouville Theory and its Applications

2008-01-15 Mathematics
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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
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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
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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.

Special Functions and Analysis of Differential Equations

2020-09-08 Mathematics
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Release : 2020-09-08
Genre : Mathematics
Kind : eBook
Book Rating : 582/5 ( reviews)

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Book Synopsis Special Functions and Analysis of Differential Equations by : Praveen Agarwal

Download or read book Special Functions and Analysis of Differential Equations written by Praveen Agarwal. This book was released on 2020-09-08. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

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