9781461436171

Ordinary Differential Equations

Mark G. Davidson, William Adkins

12th Edition

Unlike other texts on differential equations, this one provides an early presentation of the Laplace transform before deploying it in the motivation and development of many of the differential equation concepts for which it is particularly well suited.

1.1

An Introduction to Differential Equations

Exercises

p.13

1.2

Direction Fields

Exercises

p.23

1.3

Separable Differential Equations

Exercises

p.41

1.4

Linear First Order Equations

Exercises

p.59

1.5

Substitutions

Exercises

p.71

1.6

Exact Equations

Exercises

p.83

1.7

Existence and Uniqueness Theorems

Exercises

p.99

2.1

Laplace Transform Method: Introduction

Exercises

p.109

2.2

Definitions, Basic Formulas, and Principles

Exercises

p.125

2.3

Partial Fractions: A Recursive Algorithm for Linear Terms

Exercises

p.139

2.4

Partial Fractions: A Recursive Algorithm for Irreducible Quadratics

Exercises

p.149

2.5

Laplace Inversion

Exercises

p.163

2.6

The Linear Spaces: Special Cases

Exercises

p.177

2.7

The Linear Spaces: The General Case

Exercises

p.185

2.8

Convolution

Exercises

p.195

3.1

Notations, Definitions, and Some Basic Rules

Exercises

p.213

3.2

Linear Independence

Exercises

p.227

3.3

Linear Homogeneous Differential Equations

Exercises

p.235

3.4

The Method of Undetermined COefficients

Exercises

p.243

3.5

The Incomplete Partial Fraction Method

Exercises

p.251

3.6

Spring Systems

Exercises

p.265

3.7

RCL Circuits

Exercises

p.273

6.1

Calculus of Discontinuous Functions

Exercises

p.393

6.2

The Heaviside Class

Exercises

p.411

6.3

Laplace Transform Method

Exercises

p.425

6.4

The Dirac Delta Function

Exercises

p.437

6.5

Undamped Motion with Periodic Input

Exercises

p.449

6.6

Periodic Functions

Exercises

p.463

6.7

First Order Equations with Periodic Input

Exercises

p.471

6.5

Undamped Motion with Periodic Input

Exercises

p.483

9.2

Linear Systems of Differential Equations

Exercises

p.645

9.3

The Matrix Exponential and its Laplace Transform

Exercises

p.655

9.4

Fulmer's Method

Exercises

p.663

9.5

Constant Coefficient Linear Systems

Exercises

p.677

9.6

The Phase Plane

Exercises

p.699

9.7

General Linear Systems

Exercises

p.719