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Front Cover 1 Title Page 4 Copyright 5 Contents 6 Preface 10 1 INTRODUCTION TO DIFFERENTIAL EQUATIONS 18 1.1 Definitions and Terminology 19 REVIEW MATERIAL 19 INTRODUCTION 19 1.2 Initial-Value Problems 30 REVIEW MATERIAL 30 INTRODUCTION 30 1.3 Differential Equations as Mathematical Models 36 REVIEW MATERIAL 36 INTRODUCTION 36 CHAPTER 1 IN REVIEW 49 2 FIRST-ORDER DIFFERENTIAL EQUATIONS 51 2.1 Solution Curves Without a Solution 52 REVIEW MATERIAL 52 INTRODUCTION 52 2.1.1 Direction Fields 52 2.1.2 Autonomous First-Order DEs 54 2.2 Separable Variables 61 REVIEW MATERIAL 61 INTRODUCTION 61 2.3 Linear Equations 70 REVIEW MATERIAL 70 INTRODUCTION 70 2.4 Exact Equations 79 REVIEW MATERIAL 79 INTRODUCTION 79 2.5 Solutions by Substitutions 87 REVIEW MATERIAL 87 INTRODUCTION 87 2.6 A Numerical Method 92 INTRODUCTION 92 CHAPTER 2 IN REVIEW 97 3 MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS 99 3.1 Linear Models 100 REVIEW MATERIAL 100 INTRODUCTION 100 3.2 Nonlinear Models 111 REVIEW MATERIAL 111 INTRODUCTION 111 3.3 Modeling with Systems of First-Order DEs 122 REVIEW MATERIAL 122 INTRODUCTION 122 CHAPTER 3 IN REVIEW 130 4 HIGHER-ORDER DIFFERENTIAL EQUATIONS 134 4.1 Preliminary Theory—Linear

Author

Dennis G. Zill

Language

EN