Ordinary Differential Equations Basics And Beyond

Author : David G. Schaeffer,John W. Cain
Publisher : Springer
Page : 542 pages
File Size : 51,6 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781493963898

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Ordinary Differential Equations: Basics and Beyond by David G. Schaeffer,John W. Cain Pdf

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).

Author : Chin-Yuan Lin
Publisher : World Scientific
Page : 555 pages
File Size : 54,5 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.

Author : Jane Cronin
Publisher : CRC Press
Page : 408 pages
File Size : 42,9 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

Author : Ravi P. Agarwal,Donal O'Regan
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 43,6 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387712765

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An Introduction to Ordinary Differential Equations by Ravi P. Agarwal,Donal O'Regan Pdf

Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.

Author : V. DHARMAIAH
Publisher : PHI Learning Pvt. Ltd.
Page : 403 pages
File Size : 48,5 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.

Author : George F. Carrier,Carl E. Pearson
Publisher : SIAM
Page : 230 pages
File Size : 42,7 Mb
Release : 1968-01-01
Category : Mathematics
ISBN : 1611971292

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Ordinary Differential Equations by George F. Carrier,Carl E. Pearson Pdf

Offers an alternative to the "rote" approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume.

Author : Shepley L. Ross
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:1334016574

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Introduction to ordinary differential equations by Shepley L. Ross Pdf

Author : Earl A. Coddington
Publisher : Courier Corporation
Page : 306 pages
File Size : 46,7 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131832

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An Introduction to Ordinary Differential Equations by Earl A. Coddington Pdf

A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background. Includes many exercises and problems, with answers. Index.

Author : Philip Hartman
Publisher : SIAM
Page : 643 pages
File Size : 41,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898715101

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Ordinary Differential Equations by Philip Hartman Pdf

Covers the fundamentals of the theory of ordinary differential equations.

Author : Earl A. Coddington
Publisher : Unknown
Page : 308 pages
File Size : 41,5 Mb
Release : 1961
Category : Differential equations
ISBN : UOM:39015001317083

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An Introduction to Ordinary Differential Equations by Earl A. Coddington Pdf

This book is meant to be a text which can be used for a first course in ordinary differential equations. The student is assumed to have a knowledge of calculus but not what is usually called advanced calculus. The aim is to give an elementary, thorough systematic introduction to the subject. All significant results are stated as theorems, and careful proofs are given. The exercises in the book serve two purposes: to develop the student's technique in solving equations, or to help sharpen the student's understanding of the mathematical structure of the subject. The exercises also introduce the student to a variety of topics not treated in the text: stability, equations with periodic coefficients, and boundary value problems.

Author : Philip Hartman
Publisher : SIAM
Page : 612 pages
File Size : 50,5 Mb
Release : 1982-01-01
Category : Mathematics
ISBN : 0898719224

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Ordinary Differential Equations by Philip Hartman Pdf

Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, this book presents the basic theory of ODEs in a general way. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems. In particular, Ordinary Differential Equations includes the proof of the Hartman-Grobman theorem on the equivalence of a nonlinear to a linear flow in the neighborhood of a hyperbolic stationary point, as well as theorems on smooth equivalences, the smoothness of invariant manifolds, and the reduction of problems on ODEs to those on "maps" (Poincaré). Audience: readers should have knowledge of matrix theory and the ability to deal with functions of real variables.

Author : Mohammed K A Kaabar
Publisher : CreateSpace Independent Publishing Platform
Page : 163 pages
File Size : 52,5 Mb
Release : 2015-01-05
Category : Mathematics
ISBN : 9781506004532

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A Friendly Introduction to Differential Equations by Mohammed K A Kaabar Pdf

In this book, there are five chapters: The Laplace Transform, Systems of Homogenous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In addition, there are exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at "Answers to Odd-Numbered Exercises" section at the end of this book. This book is a very useful for college students who studied Calculus II, and other students who want to review some concepts of differential equations before studying courses such as partial differential equations, applied mathematics, and electric circuits II.

Author : Edward L. Ince
Publisher : Courier Corporation
Page : 576 pages
File Size : 44,6 Mb
Release : 2012-04-27
Category : Mathematics
ISBN : 9780486158211

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Ordinary Differential Equations by Edward L. Ince Pdf

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

Author : R. Grimshaw
Publisher : CRC Press
Page : 342 pages
File Size : 51,7 Mb
Release : 1991-03-06
Category : Mathematics
ISBN : 0849386071

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Nonlinear Ordinary Differential Equations by R. Grimshaw Pdf

Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

Author : Bindhyachal Rai,D. P. Choudhury
Publisher : Alpha Science Int'l Ltd.
Page : 292 pages
File Size : 40,7 Mb
Release : 2005
Category : Computers
ISBN : 1842652427

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Ordinary Differential Equations by Bindhyachal Rai,D. P. Choudhury Pdf

"This textbook primarily intended for Undergraduate, Honours and Engineering courses as well as NET/GATE and other competitive examinations presupposes no background other than elementary calculus. All the methods given in the book are explained with the help of solved examples. A large number of unsolved exercises have also been provided on each topic."--BOOK JACKET.