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Author :
Publisher :
ISBN 13 : 9788020004239
Total Pages : 320 pages
Book Rating : 4.0/5 (42 download)
Download or read book Global Properties of Linear Ordinary Differential Equations written by and published by . This book was released on 1991 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frantisek Neuman
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)
Download or read book Global Properties of Linear Ordinary Differential Equations written by Frantisek Neuman and published by Springer. This book was released on 1991 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an authoritative, unified overview of the methods and results concerning the global properties of linear differential equations of order n (n>=2). It does not, however, seek to be comprehensive. Rather, it contains a selection of results which richly illustrate the unified approach presented. By making use of recent methods and results from many different areas of mathematics and by introducing several original methods, global solutions of problems previously studied only locally are given. The structure of global transformations is described algebraically, and a new geometrical approach is introduced which leads to global canonical forms suitable for Cartan's moving frame-of-reference method. The theory discussed also provides effective tools for solving some open problems, especially relating to the distribution of zeros of solutions. In addition, the theory of functional equations plays an important role in studying the asymptotic behaviour of solutions. Applications to differential geometry and functional equations are also described. The volume is largely self-contained. This book is for mathematicians, computer scientists, physicists, chemists, engineers, and others whose work involves the use of linear differential equations.
Author : Charles A. Stuart
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.:/5 (554 download)
Download or read book Global Properties of Components of Solutions of Non-linear Second Order Ordinary Differential Equations on the Half-line written by Charles A. Stuart and published by . This book was released on 1973 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albert L. Rabenstein
Publisher : Academic Press
ISBN 13 : 1483226220
Total Pages : 444 pages
Book Rating : 4.4/5 (832 download)
Download or read book Introduction to Ordinary Differential Equations written by Albert L. Rabenstein and published by Academic Press. This book was released on 2014-05-12 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.
Author :
Publisher : Elsevier
ISBN 13 : 0080871291
Total Pages : 307 pages
Book Rating : 4.0/5 (88 download)
Download or read book Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient written by and published by Elsevier. This book was released on 1975-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Author : M. Kohno
Publisher : Springer Science & Business Media
ISBN 13 : 9401146055
Total Pages : 539 pages
Book Rating : 4.4/5 (11 download)
Download or read book Global Analysis in Linear Differential Equations written by M. Kohno and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.
Author : Ravi P Agarwal
Publisher : World Scientific
ISBN 13 : 9814505625
Total Pages : 601 pages
Book Rating : 4.8/5 (145 download)
Download or read book Recent Trends In Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1992-05-07 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series aims at reporting new developments of a high mathematical standard and of current interest. Each volume in the series shall be devoted to mathematical analysis that has been applied, or potentially applicable to the solutions of scientific, engineering, and social problems. The first volume of WSSIAA contains 42 research articles on differential equations by leading mathematicians from all over the world. This volume has been dedicated to V Lakshmikantham on his 65th birthday for his significant contributions in the field of differential equations.
Author : J. Kurzweil
Publisher : Elsevier
ISBN 13 : 1483297659
Total Pages : 441 pages
Book Rating : 4.4/5 (832 download)
Download or read book Ordinary Differential Equations written by J. Kurzweil and published by Elsevier. This book was released on 2014-06-28 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.
Author : Jane Cronin
Publisher : CRC Press
ISBN 13 : 1420014935
Total Pages : 408 pages
Book Rating : 4.4/5 (2 download)
Download or read book Ordinary Differential Equations written by Jane Cronin and published by CRC Press. This book was released on 2007-12-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
Author : Robert Mattheij
Publisher : SIAM
ISBN 13 : 0898715318
Total Pages : 408 pages
Book Rating : 4.8/5 (987 download)
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems.
Author : L. S. Pontryagin
Publisher : Elsevier
ISBN 13 : 1483156494
Total Pages : 305 pages
Book Rating : 4.4/5 (831 download)
Download or read book Ordinary Differential Equations written by L. S. Pontryagin and published by Elsevier. This book was released on 2014-05-15 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Author : A. Canada
Publisher : Elsevier
ISBN 13 : 0080532829
Total Pages : 709 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of Differential Equations: Ordinary Differential Equations written by A. Canada and published by Elsevier. This book was released on 2004-09-09 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.
Author : Albert L. Rabenstein
Publisher : Academic Press
ISBN 13 : 1483263851
Total Pages : 537 pages
Book Rating : 4.4/5 (832 download)
Download or read book Introduction to Ordinary Differential Equations written by Albert L. Rabenstein and published by Academic Press. This book was released on 2014-05-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Ordinary Differential Equations, Second Edition provides an introduction to differential equations. This book presents the application and includes problems in chemistry, biology, economics, mechanics, and electric circuits. Organized into 12 chapters, this edition begins with an overview of the methods for solving single differential equations. This text then describes the important basic properties of solutions of linear differential equations and explains higher-order linear equations. Other chapters consider the possibility of representing the solutions of certain linear differential equations in terms of power series. This book discusses as well the important properties of the gamma function and explains the stability of solutions and the existence of periodic solutions. The final chapter deals with the method for the construction of a solution of the integral equation and explains how to establish the existence of a solution of the initial value system. This book is a valuable resource for mathematicians, students, and research workers.
Author : V.V. Filippov
Publisher : Springer Science & Business Media
ISBN 13 : 940170841X
Total Pages : 536 pages
Book Rating : 4.4/5 (17 download)
Download or read book Basic Topological Structures of Ordinary Differential Equations written by V.V. Filippov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Stefan Schwabik
Publisher : World Scientific
ISBN 13 : 9814505048
Total Pages : 400 pages
Book Rating : 4.8/5 (145 download)
Download or read book Generalized Ordinary Differential Equations written by Stefan Schwabik and published by World Scientific. This book was released on 1992-10-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations. For this purpose, a generalized form of the integral based on integral sums is defined. The theory of generalized differential equations based on this integral is then used, for example, to cover differential equations with impulses or measure differential equations. Solutions of generalized differential equations are found to be functions of bounded variations.The book may be used for a special undergraduate course in mathematics or as a postgraduate text. As there are currently no other special research monographs or textbooks on this topic in English, this book is an invaluable reference text for those interested in this field.
Author : Donal O'Regan
Publisher : Springer Science & Business Media
ISBN 13 : 9401715173
Total Pages : 207 pages
Book Rating : 4.4/5 (17 download)
Download or read book Existence Theory for Nonlinear Ordinary Differential Equations written by Donal O'Regan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : W. N. Everitt
Publisher : Springer
ISBN 13 : 354039561X
Total Pages : 748 pages
Book Rating : 4.5/5 (43 download)
Download or read book Ordinary and Partial Differential Equations written by W. N. Everitt and published by Springer. This book was released on 2006-11-15 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt:
