Student Solutions Manual for

Written by the authors, the Student Solutions Manual contains worked solutions to all of the odd-numbered exercises in the text.

First-Order Differential Equations

1

(62)

Modeling via Differential Equations

2

(3)

Analytic Technique: Separation of Variables

5

(10)

Qualitative Technique: Slope Fields

15

(3)

Numerical Technique: Euler's Method

18

(3)

Existence and Uniqueness of Solutions

21

(5)

Equilibria and the Phase Line

26

(5)

Bifurcations

31

(6)

Linear Equations

37

(8)

Integrating Factors for Linear Equations

45

(18)

Review Exercises

54

(9)

First-Order Systems

63

(22)

Modeling via Systems

64

(2)

The Geometry of Systems

66

(6)

Analytic Methods for Special Systems

72

(5)

Euler's Method for Systems

77

(3)

The Lorenz Equations

80

(5)

Review Exercises

81

(4)

Linear Systems

85

(74)

Properties of Linear Systems and The Linearity Principle

86

(6)

Straight-Line Solutions

92

(11)

Phase Planes for Linear Systems with Real Eigenvalues

103

(11)

Complex Eigenvalues

114

(7)

Special Cases: Repeated and Zero Eigenvalues

121

(9)

Second-Order Linear Equations

130

(10)

The Trace-Determinant Plane

140

(4)

Linear Systems in Three Dimensions

144

(15)

Review Exercises

152

(7)

Forcing and Resonance

159

(36)

Forced Harmonic Oscillators

160

(13)

Sinusoidal Forcing

173

(7)

Undamped Forcing and Resonance

180

(6)

Amplitude and Phase of the Steady State

186

(2)

The Tacoma Narrows Bridge

188

(7)

Review Exercises

189

(6)

Nonlinear Systems

195

(44)

Equilibrium Point Analysis

196

(13)

Qualitative Analysis

209

(6)

Hamiltonian Systems

215

(4)

Dissipative Systems

219

(7)

Nonlinear Systems in Three Dimensions

226

(2)

Periodic Forcing of Nonlinear Systems and Chaos

228

(11)

Review Exercises

230

(9)

Laplace Transforms

239

(40)

Laplace Transforms

240

(8)

Discontinuous Functions

248

(6)

Second-Order Equations

254

(10)

Delta Functions and Impulse Forcing

264

(2)

Convolutions

266

(4)

The Qualitative Theory of Laplace Transforms

270

(9)

Review Exercises

271

(8)

Numerical Methods

279

(20)

Numerical Error in Euler's Method

280

(10)

Improving Euler's Method

290

(4)

The Runge-Kutta Method

294

(2)

The Effects of Finite Arithmetic

296

(3)

Review Exercises

296

(3)

Discrete Dynamical Systems

299

(12)

The Discrete Logistic Equation

300

(2)

Fixed Points and Periodic Points

302

(3)

Bifurcations

305

(2)

Chaos

307

(4)

Review Exercises

308

(3)

Appendices

311

(11)

A Changing Variables

312

(10)

B The Ultimate Guess

322

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Student Solutions Manual for Blanchard/Devaney/Hall’s Differential Equations, 3rd

Summary

Table of Contents

Supplemental Materials