Direct And Inverse Sturm Liouville Problems
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Direct And Inverse Sturm Liouville Problems
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Author : Vladislav V. Kravchenko
language : en
Publisher: Springer Nature
Release Date : 2020-07-28
Direct And Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-28 with Mathematics categories.
This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Direct And Inverse Sturm Liouville Problems Of Order Four
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Author : Amornrat Rattana
language : en
Publisher:
Release Date : 2013
Direct And Inverse Sturm Liouville Problems Of Order Four written by Amornrat Rattana and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Inverse Sturm Liouville Problems
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Author : B. M. Levitan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-07-12
Inverse Sturm Liouville Problems written by B. M. Levitan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Mathematics categories.
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Solutions Of Direct And Inverse Sturm Liouville Problems
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Author : B. B. Upeksha P. Perera
language : en
Publisher:
Release Date : 2021*
Solutions Of Direct And Inverse Sturm Liouville Problems written by B. B. Upeksha P. Perera and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021* with categories.
Solutions Of Direct And Inverse Sturm Liouville Problems
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Author : B. B. Upeksha P. Perera
language : en
Publisher:
Release Date : 2021*
Solutions Of Direct And Inverse Sturm Liouville Problems written by B. B. Upeksha P. Perera and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021* with categories.
Sturm Liouville Theory
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Author : Werner O. Amrein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Sturm Liouville Theory written by Werner O. Amrein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Mathematics categories.
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.
Sturm Liouville Theory And Its Applications
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Author : Mohammed Al-Gwaiz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-21
Sturm Liouville Theory And Its Applications written by Mohammed Al-Gwaiz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-21 with Mathematics categories.
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.
Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations
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Author : Alexander G. Megrabov
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-24
Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations written by Alexander G. Megrabov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.
Operator Theory And Harmonic Analysis
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Author : Alexey N. Karapetyants
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Operator Theory And Harmonic Analysis written by Alexey N. Karapetyants and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Inverse Problems For Fractional Partial Differential Equations
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Author : Barbara Kaltenbacher
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-17
Inverse Problems For Fractional Partial Differential Equations written by Barbara Kaltenbacher and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-17 with Mathematics categories.
As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.