9780321816252

Differential Equations: Computing and Modeling

C. Henry Edwards

5th Edition

This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts

1.1

Differential Equations and Mathematical Methods

Problems

p.8

1.2

Integrals as General and Particular Solutions

Problems

p.15

1.3

Slope Fields and Solution Curves

Problems

p.24

1.4

Separable Equations and Applications

Problems

p.40

1.5

Linear First-Order Equations

Problems

p.53

1.6

Substitution Methods and Exact Equations

Problems

p.69

Review Problems

p.74

3.1

Introduction: Second-Order Linear Equations

Problems

p.147

3.2

General Solutions of Linear Equations

Problems

p.159

3.3

Homogeneous Equations with Constant Coefficients

Problems

p.170

3.4

Mechanical Vibrations

Problems

p.181

3.5

Nonhomogeneous Equations and Undetermined Coeffcients

Problems

p.195

3.6

Forced Oscillations and Resonance

Problems

p.206

3.7

Electrical Circuits

Problems

p.215

3.8

Endpoint Problems and Eigenvalues

Problems

p.226

5.1

Matrices and Linear Systems

Problems

p.279

5.2

The Eigenvalue Method for Homogeneous Systems

Problems

p.293

5.3

A Gallery of Solution Curves of Linear Systems

Problems

p.317

5.4

Second-Order Systems and Mechanical Applications

Problems

p.331

5.5

Multiple Eigenvalue Solutions

Problems

p.346

5.6

Matrix Exponentials and Linear Systems

Problems

p.360

5.7

Nonhomogeneous Linear Systems

Problems

p.369

7.1

Laplace Transforms and Inverse Transforms

Problems

p.445

7.2

Transformation of Initial Value Problems

Problems

p.456

7.3

Translation and Partial Fractions

Problems

p.464

7.4

Derivatives, Integrals, and Products of Transforms

Problems

p.473

7.5

Periodic and Piecewise Continuous Input Functions

Problems

p.482

7.6

Impulses and Delta Functions

Problems

p.492