Functional Dynamic Equations On Time Scales
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Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15
Dynamic Equations On Time Scales written by Martin Bohner 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 2001-06-15 with Language Arts & Disciplines categories.
The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of measure chain theory has led to several important applications, e.g., in the study of insect population models, neural networks, heat transfer, and epidemic models. Key features of the book: * Introduction to measure chain theory; discussion of its usefulness in allowing for the simultaneous development of differential equations and difference equations without having to repeat analogous proofs * Many classical formulas or procedures for differential and difference equations cast in a new light * New analogues of many of the "special functions" studied * Examination of the properties of the "exponential function" on time scales, which can be defined and investigated using a particularly simple linear equation * Additional topics covered: self-adjoint equations, linear systems, higher order equations, dynamic inequalities, and symplectic dynamic systems * Clear, motivated exposition, beginning with preliminaries and progressing to more sophisticated text * Ample examples and exercises throughout the book * Solutions to selected problems Requiring only a first semester of calculus and linear algebra, Dynamic Equations on Time Scales may be considered as an interesting approach to differential equations via exposure to continuous and discrete analysis. This approach provides an early encounter with many applications in such areas as biology, physics, and engineering. Parts of the book may be used in a special topics seminar at the senior undergraduate or beginning graduate levels. Finally, the work may
Functional Dynamic Equations On Time Scales
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Author : Svetlin G. Georgiev
language : en
Publisher: Springer
Release Date : 2019-05-03
Functional Dynamic Equations On Time Scales written by Svetlin G. Georgiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-03 with Mathematics categories.
This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.
Dynamic Inequalities On Time Scales
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Author : Ravi Agarwal
language : en
Publisher: Springer
Release Date : 2014-10-30
Dynamic Inequalities On Time Scales written by Ravi Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with Mathematics categories.
This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.
Advances In Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-06
Advances In Dynamic Equations On Time Scales written by Martin Bohner 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 2002-12-06 with Mathematics categories.
Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.
Generalized Ordinary Differential Equations In Abstract Spaces And Applications
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Author : Everaldo M. Bonotto
language : en
Publisher: John Wiley & Sons
Release Date : 2021-09-15
Generalized Ordinary Differential Equations In Abstract Spaces And Applications written by Everaldo M. Bonotto and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-15 with Mathematics categories.
GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Dynamic Equations On Time Scales And Applications
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Author : Ravi P Agarwal
language : en
Publisher: CRC Press
Release Date : 2024-10-18
Dynamic Equations On Time Scales And Applications written by Ravi P Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-18 with Mathematics categories.
This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales Connects several new areas of dynamic equations on time scales with applications in different fields Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics
Functional Differential Equations And Dynamic Equations On Time Scales
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Author : Pierluigi Benevieri
language : en
Publisher: Springer Nature
Release Date : 2025-05-23
Functional Differential Equations And Dynamic Equations On Time Scales written by Pierluigi Benevieri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-23 with Mathematics categories.
This volume presents recent advances in the field of dynamic equations on time scales and functional differential equations, with a focus on how these topics can be used to describe phenomena in continuum mechanics. Chapters investigate important aspects of these equations, such as asymptotic behavior and the qualitative properties of their solutions. Specific topics covered include: Ulam stability for dynamic equations Generalized ordinary differential equations Singular control systems on time scales Bresse systems Functional Differential Equations and Dynamic Equations on Time Scales will be a valuable resource for graduate students and researchers who work in these areas.
Nonoscillation And Oscillation
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Author : Ravi P. Agarwal
language : en
Publisher:
Release Date : 2004
Nonoscillation And Oscillation written by Ravi P. Agarwal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Scaling Of Differential Equations
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Author : Hans Petter Langtangen
language : en
Publisher: Springer
Release Date : 2016-06-15
Scaling Of Differential Equations written by Hans Petter Langtangen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-15 with Mathematics categories.
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Mathematics Of Fuzzy Sets And Fuzzy Logic
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Author : Barnabas Bede
language : en
Publisher: Springer
Release Date : 2012-12-14
Mathematics Of Fuzzy Sets And Fuzzy Logic written by Barnabas Bede and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.