Ordinary Differential Equations In Rn
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Ordinary Differential Equations In Rn
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Author : Livio C. Piccinini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ordinary Differential Equations In Rn written by Livio C. Piccinini 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 2012-12-06 with Mathematics categories.
During the fifties, one of the authors, G. Stampacchia, had prepared some lecture notes on ordinary differential equations for a course in ad analysis. These remained for a long time unused because he was no vanced longer very interested in the study of such equations. We now see, though, that numerous applications to biology, chemistry, economics, and medicine have recently been added to the traditional ones in mechanics; also, there has been in these last years a reemergence of interest in nonlinear analy sis, of which the theory of ordinary differential euqations is one of the principal sources of methods and problems. Hence the idea to write a book. Our text, based on the old notes and experience gained in many courses, seminars, and conferences, both in Italy and abroad, aims to give a simple and rapid introduction to the various themes, problems, and methods of the theory of ordinary differential equations. The book has been conceived in such a way so that even the reader who has merely had a first course in calculus may be able to study it and to obtain a panoramic vision of the theory. We have tried to avoid abstract formalism, preferring instead a discursive style, which should make the book accessible to engineers and physicists without specific preparation in modern mathematics. For students of mathematics, it pro vides motivation for the subject of more advanced analysis courses.
Ordinary Differential Equations In Rn
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Author : Livio C. Piccinini
language : en
Publisher: Springer
Release Date : 2011-11-08
Ordinary Differential Equations In Rn written by Livio C. Piccinini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-08 with Mathematics categories.
During the fifties, one of the authors, G. Stampacchia, had prepared some lecture notes on ordinary differential equations for a course in ad analysis. These remained for a long time unused because he was no vanced longer very interested in the study of such equations. We now see, though, that numerous applications to biology, chemistry, economics, and medicine have recently been added to the traditional ones in mechanics; also, there has been in these last years a reemergence of interest in nonlinear analy sis, of which the theory of ordinary differential euqations is one of the principal sources of methods and problems. Hence the idea to write a book. Our text, based on the old notes and experience gained in many courses, seminars, and conferences, both in Italy and abroad, aims to give a simple and rapid introduction to the various themes, problems, and methods of the theory of ordinary differential equations. The book has been conceived in such a way so that even the reader who has merely had a first course in calculus may be able to study it and to obtain a panoramic vision of the theory. We have tried to avoid abstract formalism, preferring instead a discursive style, which should make the book accessible to engineers and physicists without specific preparation in modern mathematics. For students of mathematics, it pro vides motivation for the subject of more advanced analysis courses.
Ordinary Differential Equations In Rn
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Author : Livio Clemente Piccinini
language : en
Publisher:
Release Date : 1982-01-01
Ordinary Differential Equations In Rn written by Livio Clemente Piccinini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Differential equations categories.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan 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 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Ordinary Differential Equations With Applications
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Author : Carmen Chicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-08
Ordinary Differential Equations With Applications written by Carmen Chicone 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 2008-04-08 with Mathematics categories.
This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.
Ordinary Differential Equations And Dynamical Systems
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Author : Gerald Teschl
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-12
Ordinary Differential Equations And Dynamical Systems written by Gerald Teschl 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 2024-01-12 with Mathematics categories.
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Ordinary Differential Equations With Applications
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Author : Ali Mason
language : en
Publisher: Scientific e-Resources
Release Date : 2018-10-20
Ordinary Differential Equations With Applications written by Ali Mason and has been published by Scientific e-Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-20 with categories.
Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.
Ordinary Differential Equations And Applications
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Author : Enrique Fernandez-cara
language : en
Publisher: World Scientific
Release Date : 2023-07-26
Ordinary Differential Equations And Applications written by Enrique Fernandez-cara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-26 with Mathematics categories.
Differential equations can bring mathematics to life, describing phenomena originating in physics, chemistry, biology, economics, and more. Used by scientists and engineers alike, differential equations are also the starting point of much purely mathematical activity. They also play a role in the formulation and resolution of problems in harmonic analysis, differential geometry, and probability calculus. A large part of functional analysis has therefore been motivated by the need to solve questions in the analysis of differential systems, as with numerical analysis.Differential equations are doubly relevant, then: as significant in many areas of mathematics, and as important machinery for applying mathematics to real-world problems. This book therefore aims to provide a rigorous introduction to the theoretical study of differential equations, and to demonstrate their utility with applications in many fields.Ordinary Differential Equations and Applications originates from several courses given by the author for decades at the University of Seville. It aims to bring together rigorous mathematical theory and the rich variety of applications for differential equations. The book examines many aspects of differential equations: their existence, uniqueness, and regularity, alongside their continuous dependence on data and parameters. Delving into permanent interpretation of the laws of differential equations, we also look at the role of data and how their solutions behave. Each chapter finishes with a collection of exercises, many of which also contain useful hints.
Singular Perturbation Methods For Ordinary Differential Equations
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Author : Robert E., Jr. O'Malley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Perturbation Methods For Ordinary Differential Equations written by Robert E., Jr. O'Malley 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 2012-12-06 with Mathematics categories.
This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.
Ordinary Differential Equations
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Author : D. Somasundaram
language : en
Publisher: CRC Press
Release Date : 2001
Ordinary Differential Equations written by D. Somasundaram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique. Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations. Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.