Theory And Examples Of Ordinary Differential Equations

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Theory and Examples of Ordinary Differential Equations

Chin-Yuan Lin
Theory and Examples of Ordinary Differential Equations Book PDF

Author : Chin-Yuan Lin
Publisher : World Scientific
Page : 555 pages
File Size : 42,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814307123

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Theory and Examples of Ordinary Differential Equations by Chin-Yuan Lin Pdf

This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.

The Qualitative Theory of Ordinary Differential Equations

Fred Brauer,John A. Nohel
The Qualitative Theory of Ordinary Differential Equations Book PDF

Author : Fred Brauer,John A. Nohel
Publisher : Courier Corporation
Page : 325 pages
File Size : 43,8 Mb
Release : 2012-12-11
Category : Mathematics
ISBN : 9780486151519

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The Qualitative Theory of Ordinary Differential Equations by Fred Brauer,John A. Nohel Pdf

Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

V. DHARMAIAH
INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION Book PDF

Author : V. DHARMAIAH
Publisher : PHI Learning Pvt. Ltd.
Page : 403 pages
File Size : 45,9 Mb
Release : 2012-09-19
Category : Mathematics
ISBN : 9788120346666

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INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION by V. DHARMAIAH Pdf

This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.

Ordinary Differential Equations

Jane Cronin
Ordinary Differential Equations Book PDF

Author : Jane Cronin
Publisher : CRC Press
Page : 408 pages
File Size : 50,7 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9781420014938

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Ordinary Differential Equations by Jane Cronin Pdf

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

Ordinary Differential Equations

Luis Barreira,Claudia Valls
Ordinary Differential Equations Book PDF

Author : Luis Barreira,Claudia Valls
Publisher : American Mathematical Society
Page : 264 pages
File Size : 53,6 Mb
Release : 2023-05-17
Category : Mathematics
ISBN : 9781470473860

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Ordinary Differential Equations by Luis Barreira,Claudia Valls Pdf

This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

Ordinary Differential Equations

Morris Tenenbaum,Harry Pollard
Ordinary Differential Equations Book PDF

Author : Morris Tenenbaum,Harry Pollard
Publisher : Courier Corporation
Page : 852 pages
File Size : 55,8 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 9780486649405

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Ordinary Differential Equations by Morris Tenenbaum,Harry Pollard Pdf

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Applications of Lie's Theory of Ordinary and Partial Differential Equations

L Dresner
Applications of Lie s Theory of Ordinary and Partial Differential Equations Book PDF

Author : L Dresner
Publisher : CRC Press
Page : 242 pages
File Size : 54,8 Mb
Release : 1998-01-01
Category : Science
ISBN : 1420050788

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Applications of Lie's Theory of Ordinary and Partial Differential Equations by L Dresner Pdf

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Partial Differential Equations

Thomas Hillen,I. E. Leonard,Henry van Roessel
Partial Differential Equations Book PDF

Author : Thomas Hillen,I. E. Leonard,Henry van Roessel
Publisher : John Wiley & Sons
Page : 610 pages
File Size : 48,8 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118438435

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Partial Differential Equations by Thomas Hillen,I. E. Leonard,Henry van Roessel Pdf

Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

The Theory of Differential Equations

Walter G. Kelley,Allan C. Peterson
The Theory of Differential Equations Book PDF

Author : Walter G. Kelley,Allan C. Peterson
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 44,7 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781441957825

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The Theory of Differential Equations by Walter G. Kelley,Allan C. Peterson Pdf

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.

Ordinary Differential Equations in Theory and Practice

Robert Mattheij,Jaap Molenaar
Ordinary Differential Equations in Theory and Practice Book PDF

Author : Robert Mattheij,Jaap Molenaar
Publisher : SIAM
Page : 423 pages
File Size : 53,9 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0898719178

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Ordinary Differential Equations in Theory and Practice by Robert Mattheij,Jaap Molenaar Pdf

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. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.

Theory of Ordinary Differential Equations

Earl A. Coddington,Norman Levinson
Theory of Ordinary Differential Equations Book PDF

Author : Earl A. Coddington,Norman Levinson
Publisher : Tata McGraw-Hill Education
Page : 456 pages
File Size : 51,8 Mb
Release : 1955
Category : Boundary value problems
ISBN : UOM:39015000978968

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Theory of Ordinary Differential Equations by Earl A. Coddington,Norman Levinson Pdf

This book has developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician. Prerequisite for this book is a knowledge of matrices and the essentials of functions in a complex variable. The book thoroughly addresses linear equations, and touches on the use of the Riemann-Stieltjes integral, and the Lebesgue integral, and the theorems required from integration theory. The problems, in some cases, give additional material not considered in the text.

Existence Theory for Nonlinear Ordinary Differential Equations

Donal O'Regan
Existence Theory for Nonlinear Ordinary Differential Equations Book PDF

Author : Donal O'Regan
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 53,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401715171

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Existence Theory for Nonlinear Ordinary Differential Equations by Donal O'Regan Pdf

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

James Morris Page
Ordinary Differential Equations Book PDF

Author : James Morris Page
Publisher : Forgotten Books
Page : 242 pages
File Size : 51,7 Mb
Release : 2015-06-16
Category : Mathematics
ISBN : 1330126661

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Ordinary Differential Equations by James Morris Page Pdf

Excerpt from Ordinary Differential Equations: With an Introduction to Lie's Theory of the Group of One Parameter This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure Mathematics. On account of the elementary character of the book, only the simpler portions of the subject have been touched upon at all; and much care has been taken to make all the developments as clear as possible - every important step being illustrated by easy examples. In one material respect, this book differs from the older text-books upon the subject in the English language: namely, in the methods employed. Ever since the discovery of the Infinitesimal Calculus, the integration of differential equations has been one of the weightiest problems that have attracted the attention of mathematicians. It is not possible to develop a method of integration for all differential equations; but it was found possible to give theories of integration for certain classes of these equations; for instance, for the homogeneous or for the linear, differential equation of the first order. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Ordinary Differential Equations with Applications

Carmen Chicone
Ordinary Differential Equations with Applications Book PDF

Author : Carmen Chicone
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 41,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780387985350

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Ordinary Differential Equations with Applications by Carmen Chicone Pdf

This graduate-level textbook offers students a rapid introduction to the language of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering.

Differential Equations: Theory and Applications

David Betounes
Differential Equations Theory and Applications Book PDF

Author : David Betounes
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 55,9 Mb
Release : 2009-10-31
Category : Mathematics
ISBN : 9781441911636

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Differential Equations: Theory and Applications by David Betounes Pdf

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.