First Order Partial 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

First Order Partial Dynamic Equations On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2024-03-05

First Order Partial Dynamic Equations On Time Scales written by Svetlin G. Georgiev and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-05 with Mathematics categories.

This book presents an introduction to the theory of first order partial dynamic equations (PDEs) on time scales. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses, but students in mathematical and physical sciences will also find many sections relevant. This book contains five chapters, and each chapter consists of results with their proofs, numerous examples, and exercises with solutions. Each chapter concludes with a section featuring advanced practical problems with solutions followed by a section on notes and references, explaining its context within existing literature. The book presents a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques, and the text of this book is presented in a readable and mathematically solid format.

Finite Difference Methods For Ordinary And Partial Differential Equations

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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01

Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Fuzzy Dynamic Equations Dynamic Inclusions And Optimal Control Problems On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Springer Nature
Release Date : 2021-07-15

Fuzzy Dynamic Equations Dynamic Inclusions And Optimal Control Problems On Time Scales written by Svetlin G. Georgiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Mathematics categories.

The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance.

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.

Partial Differential Equations In Action

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Author : Sandro Salsa
language : en
Publisher: Springer
Release Date : 2015-04-24

Partial Differential Equations In Action written by Sandro Salsa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Partial Differential Equations

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Author : Vladimir A. Tolstykh
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-06-08

Partial Differential Equations written by Vladimir A. Tolstykh 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 2020-06-08 with Mathematics categories.

This is a clear, rigorous and self-contained introduction to PDEs for a semester-based course on the topic. For the sake of smooth exposition, the book keeps the amount of applications to a minimum, focusing instead on the theoretical essentials and problem solving. The result is an agile compendium of theorems and methods - the ideal companion for any student tackling PDEs for the first time. Vladimir Tolstykh is a professor of mathematics at Istanbul Arel University. He works in group theory and model-theoretic algebra. Dr. Tolstykh received his Ph.D. in Mathematics from the Ural Institute of Mathematics and Mechanics (Ekaterinburg (Russia) in 1992 and his Doctor of Science degree in Mathematics from the Sobolev Institute of Mathematics (Novosibirsk, Russia) in 2007.

Differential Equations

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Author : Gaston M. N'Guerekata
language : en
Publisher:
Release Date : 2012

Differential Equations written by Gaston M. N'Guerekata and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Differential equations categories.

This book presents and discusses new developments in the study of differential equations. Topics discussed include pseudo almost automorphic solutions for some non-linear differential equations; positive solutions for p-laplacian dynamic delay differential equations on time scales; semi-linear fractional differential equations; positive solutions for a class of second-order impulsive singular differential equations in banach spaces and non-linear hyperbolic second-order partial differential equations with delay.

A First Course In The Numerical Analysis Of Differential Equations

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Author : A. Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2009

A First Course In The Numerical Analysis Of Differential Equations written by A. Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

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.