Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition

Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition

3rd Edition | ISBN: 9781118981221 / 1118981227

1,184

expert-verified solutions in this book

Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition
Buy on Amazon.com

3rd Edition | ISBN: 9781118981221 / 1118981227

1,184

expert-verified solutions in this book

Buy on Amazon.com

Table of Contents

Chapter 1

Introduction

1-1 Mathematical Models and Solutions Problems p.10
1-2 Qualitative Methods: Phase Lines and Direction Fields Problems p.25
1-3 Definitions, Classification, and Terminology Problems p.35

Chapter 2

First Order Differential Equations

2-1 Separable Equations Problems p.44
2-2 Linear Equations: Method of Integrating Factors Problems p.54
2-3 Modeling with First Order Equations Problems p.65
2-4 Differences Between Linear and Nonlinear Equations Problems p.79
2-5 Autonomous Equations and Population Dynamics Problems p.91
2-6 Exact Equations and Integrating Factors Problems p.100
2-7 Substitution Methods Problems p.108
Project 1 Problems p.111
Project 2 Problems p.113
Project 3 Problems p.115

Chapter 3

Systems Of Two First Order Equations

3-1 Systems of Two Linear Algebraic Equations Problems p.128
3-2 Systems of Two First Order Linear Differential Equations Problems p.142
3-3 Homogeneous Linear Systems with Constant Coefficients Problems p.165
3-4 Complex Eigenvalues Problems p.177
3-5 Repeated Eigenvalues Problems p.188
3-6 A Brief Introduction to Nonlinear Systems Problems p.196
Project 1 Problems p.199
Project 2 Problems p.201

Chapter 4

Second Order Linear Equations

4-1 Definitions and Examples Problems p.214
4-2 Theory of Second Order Linear Homogeneous Equations Problems p.226
4-3 Linear Homogeneous Equations with Constant Coefficients Problems p.239
4-4 Mechanical and Electrical Vibrations Problems p.250
4-5 Nonhomogeneous Equations; Method of Undetermined Coefficients Problems p.260
4-6 Forced Vibrations, Frequency Response, and Resonance Problems p.272
4-7 Variation of Parameters Problems p.280
Project 1 Problems p.286
Project 2 Problems p.287
Project 3 Problems p.288
Project 4 Problems p.291

Chapter 5

The Laplace Transform

5-1 Definition of the Laplace Transform Problems p.302
5-2 Properties of the Laplace Transform Problems p.309
5-3 The Invers Laplace Transform Problems p.319
5-4 Solving Differential Equations with Laplace Transform Problems p.327
5-5 Discontinuous Functions and Periodic Functions Problems p.336
5-6 Differential Equations with Discontinuous Forcing Functions Problems p.342
5-7 Impulse Functions Problems p.350
5-8 Convolution Integrals and Their Applications Problems p.359
5-9 Linear Systems and Feedback Control Problems p.369
Project 1 Problems p.372
Project 2 Problems p.375

Chapter 6

Systems Of First Order Linear Equations

6-1 Definitions and Examples Problems p.388
6-2 Basic Theory of First Order Linear Systems Problems p.398
6-3 Homogeneous Linear Systems with Constant Coefficients Problems p.408
6-4 Nondefective Matrices with Complex Eigenvalues Problems p.419
6-5 Fundamental Matrices and Exponential of a Matrix Problems p.430
6-6 Nonhomogeneous Linear Systems Problems p.436
6-7 Defective Matrices Problems p.444
Project 1 Problems p.447
Project 2 Problems p.455

Chapter 7

Nonlinear Differential Equations And Stability

7-1 Autonomous Systems and Stability Problems p.464
7-2 Almost Linear Systems Problems p.475
7-3 Competing Species Problems p.486
7-4 Predator-Prey Equations Problems p.494
7-5 Periodic Solutions and Limit Cycles Problems p.504
7-6 Chaos and Strange Attractors: The Lorenz Equations Problems p.512
Project 1 Problems p.516
Project 2 Problems p.517
Project 3 Problems p.518

Chapter 8

Numerical Methods

8-1 Numerical Approximations: Euler's Method Problems p.529
8-2 Accuracy of Numerical Methods Problems p.536
8-3 Improved Euler and Runge-Kutta Methods Problems p.545
8-4 Numerical Methods for Systems of First Order Equations Problems p.549
Project 1 Problems p.551
Project 2 Problems p.553

Chapter Appendix A

Matrices And Linear Algebra

A-1 Matrices Problems p.563
A-2 Systems of Linear Algebraic Equations, Linear Independence, and Rank Problems p.580
A-3 Determinants and Inverse Problems p.589
A-4 The Eigenvalue Problem Problems p.599
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