Basic Topological Structures Of Ordinary Differential Equations
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Basic Topological Structures Of Ordinary Differential Equations
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Author : V.V. Filippov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Basic Topological Structures Of Ordinary Differential Equations written by V.V. Filippov 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 2013-03-09 with Mathematics categories.
The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist.
Basic Topological Structures Of Ordinary Differential Equations
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Author : V. V. Filippov
language : en
Publisher:
Release Date : 2014-01-15
Basic Topological Structures Of Ordinary Differential Equations written by V. V. Filippov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Ordinary Differential Equations And Applications Ii With Maple Illustrations
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Author : Benjamin Oyediran Oyelami
language : en
Publisher: Bentham Science Publishers
Release Date : 2024-12-19
Ordinary Differential Equations And Applications Ii With Maple Illustrations written by Benjamin Oyediran Oyelami and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-19 with Mathematics categories.
Ordinary Differential Equations and Applications II: With Maple Illustrations integrates fundamental theories of Ordinary Differential Equations (ODEs) with practical applications and Maple-based solutions. This comprehensive textbook covers vector-valued differential equations, matrix solutions, stability methods, and periodic systems. Using Maple and MapleSim software, readers learn symbolic solutions, plotting techniques, 2D/3D animation for ODE problems, and simulations for engineering systems. This book is ideal for undergraduate and postgraduate students in mathematics, physics, economics, and engineering, as well as researchers and professionals needing advanced applications of ODEs. Key Features: - Comprehensive introduction to ODE concepts and real-life applications - Solutions for initial value problems using Maple and MapleSim software - Analysis of stability using Routh-Hurwitz and Lyapunov methods - Models of neural firing, avian influenza, and biological populations - Practical guidance on MapleSim for multi-domain simulations, code generation, and Monte Carlo simulation
Order Structure And Topological Methods In Nonlinear Partial Differential Equations
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Author : Yihong Du
language : en
Publisher: World Scientific
Release Date : 2006
Order Structure And Topological Methods In Nonlinear Partial Differential Equations written by Yihong Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems. The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time. Sample Chapter(s). Chapter 1: Krein-Rutman Theorem and the Principal Eigenvalue (128 KB). Contents: KreinOCoRutman Theorem and the Principal Eigenvalue; Maximum Principles Revisited; The Moving Plane Method; The Method of Upper and Lower Solutions; The Logistic Equation; Boundary Blow-Up Problems; Symmetry and Liouville Type Results Over Half and Entire Spaces. Readership: Researchers and postgraduate students in partial differential equations."
A Short Course In Ordinary Differential Equations
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Author : Qingkai Kong
language : en
Publisher: Springer
Release Date : 2014-10-21
A Short Course In Ordinary Differential Equations written by Qingkai Kong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-21 with Mathematics categories.
This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.
Ordinary Differential Equations Basics And Beyond
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Author : David G. Schaeffer
language : en
Publisher: Springer
Release Date : 2016-11-10
Ordinary Differential Equations Basics And Beyond written by David G. Schaeffer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Mathematics categories.
This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
Topological Methods For Delay And Ordinary Differential Equations
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Author : Pablo Amster
language : en
Publisher: Springer Nature
Release Date : 2024-08-12
Topological Methods For Delay And Ordinary Differential Equations written by Pablo Amster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-12 with Mathematics categories.
This volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more. Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats, non-Newtonian fluid flow, and flows in phase space. Topological Methods for Delay and Ordinary Differential Equations will be a valuable resource for researchers interested in differential equations, functional analysis, topology, and the applied sciences.
Topological Fixed Point Theory Of Multivalued Mappings
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Author : Lech Górniewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Topological Fixed Point Theory Of Multivalued Mappings written by Lech Górniewicz 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 2013-11-11 with Mathematics categories.
This book is an attempt to give a systematic presentation of results and meth ods which concern the fixed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to study ing topological methods in the fixed point theory of multivalued mappings and applications, mainly to differential inclusions. Thus in Chapter III the approximation (on the graph) method in fixed point theory of multi valued mappings is presented. Chapter IV is devoted to the homo logical methods and contains more general results, e. g. , the Lefschetz Fixed Point Theorem, the fixed point index and the topological degree theory. In Chapter V applications to some special problems in fixed point theory are formulated. Then in the last chapter a direct application's to differential inclusions are presented. Note that Chapter I and Chapter II have an auxiliary character, and only results con nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the fixed point theory. In the last section of our book (see Section 75) we give a bibliographical guide and also signal some further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and com mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. Gorka, M. Gorniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
Air Force Research Objectives
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Author : United States. Air Force. Office of Aerospace Research
language : en
Publisher:
Release Date : 1963
Air Force Research Objectives written by United States. Air Force. Office of Aerospace Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Military research categories.
New Foundations For Applied Electromagnetics The Spatial Structure Of Electromagnetic Fields
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Author : Said Mikki
language : en
Publisher: Artech House
Release Date : 2016-05-31
New Foundations For Applied Electromagnetics The Spatial Structure Of Electromagnetic Fields written by Said Mikki and has been published by Artech House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-31 with Technology & Engineering categories.
This comprehensive new resource focuses on applied electromagnetics and takes readers beyond the conventional theory with the use of contemporary mathematics to improve the practical use of electromagnetics in emerging areas of field communications, wireless power transfer, metamaterials, MIMO and direction-of-arrival systems. The book explores the existing and novel theories and principles of electromagnetics in order to help engineers analyze and design devices for today's applications in wireless power transfers, NFC, and metamaterials. This book is organized into clear and logical sections spanning from fundamental theory, to applications, promoting clear understanding through-out. This resource presents the theory of electromagnetic near fields including chapters on reactive energy, spatial and spectral theory, the scalar antenna, and the morphogenesis of electromagnetic radiation in the near field zone. The Antenna Current Green's Function Formalism is explored with an emphasis on the foundations, the organic interrelationships between the fundamental operational modes of general antenna systems, and the spectral approach to antenna-to-antenna interactions. The book offers perspective on nonlocal metamaterials, including the material response theory, the far-field theory, and the near-field theory.