1550078481-Ordinary_Differential_Equations__Roberts_

Contents

Preface

1 Introduction

1.1 Historical Prologue

1.2 Definit ions and Terminology

1.3 Solutions and Problems

1.4 A Nobel Prize Winning Application

2 The Initial Value Problem y' = f(x, y) ; y(c) = d

2. l Direction Fields....

2.2 Fundamental Theorems

2.3 Solution of Simple First-Order Differential Equations

2.3.l Solution of y' = g(x) ............

2.3.2 Solution of the Separable Equation y' = g(x)/h(y)

2.3.3 Solution of the Linear Equation y' = a(x)y + b(x)

2.4 Numerical Solution

2.4.1 Single-Step Methods

2.4.l.l Taylor Series Method

2.4.l.2 Runge-Kutta Methods

2.4.2 Multistep Methods......

2.4.2. 1 Adams-Bashforth Methods

2.4.2.2 Nystrom Methods...

2.4.2.3 Adams-Moulton Methods

2.4.3 Predictor-Corrector Methods.

2.4.4 Pitfalls of Numerical Methods

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