Introductory Differential Equations

Preface

• Technology
• Applications
• Style
• Features
• Pedagogical Features
• Content

Chapter 1: Introduction to Differential Equations

• Abstract
• 1.1 Introduction to Differential Equations: Vocabulary
• Exercises 1.1
• 1.2 A Graphical Approach to Solutions: Slope Fields and Direction Fields
• Exercises 1.2
• Chapter 1 Summary: Essential Concepts and Formulas
• Chapter 1 Review Exercises

Chapter 2: First-Order Equations

• Abstract
• 2.1 Introduction to First-Order Equations
• Exercises 2.1
• 2.2 Separable Equations
• Exercises 2.2
• 2.3 First-Order Linear Equations
• Exercises 2.3
• 2.4 Exact Differential Equations
• Exercises 2.4
• 2.5 Substitution Methods and Special Equations
• Exercises 2.5
• 2.6 Numerical Methods for First-Order Equations
• Exercises 2.6
• Chapter 2 Summary: Essential Concepts and Formulas
• Chapter 2 Review Exercises
• Differential Equations at Work

Chapter 3: Applications of First-Order Differential Equations

• Abstract
• 3.1 Population Growth and Decay
• Exercises 3.1
• 3.2 Newton’s Law of Cooling and Related Problems
• Exercises 3.2
• 3.3 Free-Falling Bodies
• Exercises 3.3
• Chapter 3 Summary: Essential Concepts and Formulas
• Chapter 3 Review Exercises
• Differential Equations at Work

Chapter 4: Higher Order Equations

• Abstract
• 4.1 Second-Order Equations: An Introduction
• Exercises 4.1
• 4.2 Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients
• Exercises 4.2
• 4.3 Solving Second-Order Linear Equations: Undetermined Coefficients
• Exercises 4.3
• 4.4 Solving Second-Order Linear Equations: Variation of Parameters
• Exercises 4.4
• 4.5 Solving Higher Order Linear Homogeneous Equations
• Exercises 4.5
• 4.6 Solving Higher Order Linear Equations: Undetermined Coefficients and Variation of Parameters
• Exercises 4.6
• 4.7 Cauchy-Euler Equations
• Exercises 4.7
• 4.8 Power Series Solutions of Ordinary Differential Equations
• Exercises 4.8
• 4.9 Series Solutions of Ordinary Differential Equations
• Exercises 4.9
• Chapter 4 Summary: Essential Concepts and Formulas
• Chapter 4 Review Exercises
• Differential Equations at Work

Chapter 5: Applications of Higher Order Differential Equations

• Abstract
• 5.1 Simple Harmonic Motion
• 5.2 Damped Motion
• 5.3 Forced Motion
• 5.4 Other Applications
• 5.5 The Pendulum Problem
• Chapter 5 Summary: Essential Concepts and Formulas
• Chapter 5 Review Exercises
• Differential Equations at Work

Chapter 6: Systems of Differential Equations

• Abstract
• 6.1 Introduction
• Exercises 6.1
• 6.2 Review of Matrix Algebra and Calculus
• Exercises 6.2
• 6.3 An Introduction to Linear Systems
• Exercises 6.3
• 6.4 First-Order Linear Homogeneous Systems With Constant Coefficients
• Exercises 6.4
• 6.5 First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters
• Exercises 6.5
• 6.6 Phase Portraits
• Exercises 6.6
• 6.7 Nonlinear Systems
• Exercises 6.7
• 6.8 Numerical Methods
• Exercises 6.8
• Chapter 6 Summary: Essential Concepts and Formulas
• Chapter 6 Review Exercises
• Differential Equations at Work

Chapter 7: Applications of Systems of Ordinary Differential Equations

• Abstract
• 7.1 Mechanical and Electrical Problems With First-Order Linear Systems
• Exercises 7.1
• 7.2 Diffusion and Population Problems With First-Order Linear Systems
• Exercises 7.2
• 7.3 Nonlinear Systems of Equations
• Exercises 7.3
• Chapter 7 Summary: Essential Concepts and Formulas
• Chapter 7 Review Exercises
• Differential Equations at Work

Chapter 8: Introduction to the Laplace Transform

• Abstract
• 8.1 The Laplace Transform: Preliminary Definitions and Notation
• Exercises 8.1
• 8.2 The Inverse Laplace Transform
• Exercises 8.2
• 8.3 Solving Initial-Value Problems with the Laplace Transform
• Exercises 8.3
• 8.4 Laplace Transforms Of Several Important Functions
• Exercises 8.4
• 8.5 The Convolution Theorem
• Exercises 8.5
• 8.6 Laplace Transform Methods for Solving Systems
• Exercises 8.6
• 8.7 Some Applications Using Laplace Transforms
• Chapter 8 Review Exercises
• Differential Equations at Work

Answers to Selected Exercises

• Exercises 1.1
• Exercises 1.2
• Chapter 1 Review Exercises
• Exercises 2.1
• Exercises 2.2
• Exercises 2.3
• Exercises 2.4
• Exercises 2.5
• Exercises 2.6
• Chapter 2 Review Exercises
• Exercises 3.1
• Exercises 3.2
• Exercises 3.3
• Chapter 3 Review Exercises
• Exercises 4.1
• Exercises 4.2
• Exercises 4.3
• Exercises 4.4
• Exercises 4.5
• Exercises 4.6
• Exercises 4.7
• Exercises 4.8
• Exercises 4.9
• Chapter 4 Review Exercises
• Exercises 5.1
• Exercises 5.2
• Exercises 5.3
• Exercises 5.4
• Exercises 5.5
• Chapter 5 Review Exercises
• Exercises 6.1
• Exercises 6.2
• Exercises 6.3
• Exercises 6.4
• Exercises 6.5
• Exercises 6.6
• Exercises 6.7
• Exercises 6.8
• Chapter 6 Review Exercises
• Exercises 7.1
• Exercises 7.2
• Exercises 7.3
• Chapter 7 Review Exercises
• Exercises 8.1
• Exercises 8.2
• Exercises 8.3
• Exercises 8.4
• Exercises 8.5
• Exercises 8.6
• Exercises 8.7
• Chapter 8 Review ExercisesIndex