1550078481-Ordinary_Differential_Equations__Roberts_

ORDINARY DIFFERENTIAl EQUATIONS Applications, Models, and Computing ...

TEXTBOOKS in MATHEMATICS Series Editor: Denny Gulick PUBLISHED TITLES ABSTRACT ALGEBRA: AN INTERACTIVE APPROACH William Paulsen ...

TEXTBOOKS in MATHEMATICS ORDINARY DIFFERENTIAl EQUATIONS APPiications, Models, and Computing Charles E. Roberts, Jr. Indiana Sta ...

MATLAB• is a trademark of The MathWorks, Inc. and is used with permission. T he MathWorks does not warrant the accuracy of the t ...

To the memory of my mother and father, Evelyn and Charles And to t hose who "light up my li fe," my wife, Imogene my children , ...

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Contents Preface 1 Introduction 1.1 Historical Prologue 1.2 Definit ions and Terminology 1.3 Solutions and Problems 1.4 A Nobel ...

viii 3 Applications of the Initial Value Problem y'=f(x, y); y(c)=d 3.1 Calculus Revisited 3.2 Learning Theory Models 3.3 Popula ...

ix - with Constant Coefficients 6 Applications of Linear Differential Equations - 6.1 Second-Order Differential Equati ...

x 10.7 P endulums 10.8 Duffing's Equation 10.9 Van der Pol's Equation 10.10 Mixture Problems.. 10.11 The Restricted Three-Body P ...

Preface Ordinary Differential Equations: Applications, Models, and Computing is an introductory level textbook for undergraduate ...

xii Solve on an interval [a, b] a vector initial value problem consisting of a system of n first-order differential equations a ...

Xlll comments. In this text, we also attempt to provide an even balance between theory, computer solution, and application. We r ...

xiv of diverse disciplines which can be written as initial value problems and then solved using numerical integration software. ...

xv In Chapter 10 we present techniques for determining the b ehavior of so- lutions to systems of first-order differential equat ...

xvi ponents. The user may view the solution values on the interval [a, b], may graph a ny subset of solution components on any s ...

XVII The second best teaching environment consists of a reg ular classroom. Prior to class, the instructor rolls a "computer-on- ...

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Chapter 1 Introduction 1.1 Historical Prologue The singular concept which characterizes calculus and simultaneously sets it apar ...

2 Ordinary Differential Equations which is equivalent to finding tangents to the curves; he also introduces into mathematics t h ...