April 13, 2021

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Ordinary Differential Equations

Ordinary Differential Equations
Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
Release Date : 1992-05-08
Category : Mathematics
Total pages :338
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Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW

Ordinary Differential Equations

Ordinary Differential Equations
Author : Morris Tenenbaum,Harry Pollard
Publisher : Courier Corporation
Release Date : 1963
Category : Mathematics
Total pages :808
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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.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Philip Hartman
Publisher : SIAM
Release Date : 2002-01-01
Category : Mathematics
Total pages :612
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Covers the fundamentals of the theory of ordinary differential equations.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Jack K. Hale
Publisher : Courier Corporation
Release Date : 2009-01-01
Category : Mathematics
Total pages :361
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This rigorous treatment prepares readers for the study of differential equations and shows them how to research current literature. It emphasizes nonlinear problems and specific analytical methods. 1969 edition.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Raza Tahir-Kheli
Publisher : Springer
Release Date : 2019-02-05
Category : Science
Total pages :408
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This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.

Modelling with Ordinary Differential Equations

Modelling with Ordinary Differential Equations
Author : T.P. Dreyer
Publisher : Routledge
Release Date : 2017-09-06
Category : Mathematics
Total pages :304
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Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Solving Ordinary Differential Equations I

Solving Ordinary Differential Equations I
Author : Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner
Publisher : Springer Science & Business Media
Release Date : 2008-04-16
Category : Mathematics
Total pages :528
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This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION
Author : V. DHARMAIAH
Publisher : PHI Learning Pvt. Ltd.
Release Date : 2012-09-19
Category : Mathematics
Total pages :420
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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

Ordinary Differential Equations
Author : D. Somasundaram
Publisher : CRC Press
Release Date : 2001
Category : Mathematics
Total pages :295
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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.

Ordinary Differential Equations

Ordinary Differential Equations
Author : David A. Sanchez
Publisher : American Mathematical Soc.
Release Date : 2002-12-31
Category : Mathematics
Total pages :132
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For the instructor or student confronting an introductory course in ordinary differential equations there is a need for a brief guide to the key concepts in the subject. Important topics like stability, resonance, existence of periodic solutions, and the essential role of continuation of solutions are often engulfed in a sea of exercises in integration, linear algebra theory, computer programming and an overdose of series expansions. This book is intended as that guide. It is more conceptual than definitive and more light-hearted than pedagogic. It covers key topics and theoretical underpinnings that are necessary for the study of rich topics like nonlinear equations or stability theory. The [Author]; has included a great many illuminating examples and discussions that uncover the conceptual heart of the matter.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Michael D. Greenberg
Publisher : John Wiley & Sons
Release Date : 2014-05-29
Category : Mathematics
Total pages :544
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Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions Systems of Nonlinear Differential Equations In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers. Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work. An Instructors Manual is available upon request. Email [email protected] for information. There is also a Solutions Manual available. The ISBN is 9781118398999.

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications
Author : Carmen Charles Chicone
Publisher : Springer Science & Business Media
Release Date : 1999
Category : Mathematics
Total pages :561
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This fast-paced introduction to the language of ODEs includes consideration of its origins and applications in science and engineering. Supplementary material provides connections between the theory and other advanced mathematical topics. Mastery of the material this book will provide a solid background for research in ODEs and applications of the theory to real world problems.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Charles Roberts
Publisher : CRC Press
Release Date : 2011-06-13
Category : Mathematics
Total pages :600
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In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations. Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions. Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors.

Ordinary Differential Equations

Ordinary Differential Equations
Author : Bhamra
Publisher : Allied Publishers
Release Date : 2021
Category :
Total pages :129
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Ordinary Differential Equations

Ordinary Differential Equations
Author : Bernd J. Schroers
Publisher : Cambridge University Press
Release Date : 2011-09-29
Category : Mathematics
Total pages :129
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Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.