Student Solutions Manual for Blanchard/Devaney/Hall's Differential Equations, 4th / Edition 4

Student Solutions Manual for Blanchard/Devaney/Hall's Differential Equations, 4th / Edition 4

by Paul Blanchard, Robert L. Devaney, Glen R. Hall
     
 

ISBN-10: 0495826723

ISBN-13: 9780495826729

Pub. Date: 05/18/2011

Publisher: Cengage Learning


Contains fully worked-out solutions to all of the odd-numbered exercises in the text.  See more details below

Overview


Contains fully worked-out solutions to all of the odd-numbered exercises in the text.

Product Details

ISBN-13:
9780495826729
Publisher:
Cengage Learning
Publication date:
05/18/2011
Edition description:
Student
Pages:
352
Sales rank:
338,886
Product dimensions:
8.40(w) x 10.80(h) x 0.90(d)

Table of Contents

1 First-Order Differential Equations 1

1.1 Modeling via Differential Equations 2

1.2 Analytic Technique: Separation of Variables 6

1.3 Qualitative Technique: Slope Fields 16

1.4 Numerical Technique: Euler's Method 20

1.5 Existence and Uniqueness of Solutions 24

1.6 Equilibria and the Phase Line 27

1.7 Bifurcations 33

1.8 Linear Equations 38

1.9 Integrating Factors for Linear Equations 46

Review Exercises 55

2 First-Order Systems 65

2.1 Modeling via Systems 66

2.2 The Geometry of Systems 68

2.3 The Damped Harmonic Oscillator 74

2.4 Additional Analytic Methods for Special Systems 77

2.5 Euler's Method for Systems 80

2.6 Existence and Uniqueness for Systems 82

2.7 The SIR Model of an Epidemic 84

2.8 The Lorenz Equations 86

Review Exercises 87

3 Linear Systems 91

3.1 Properties of Linear Systems and The Linearity Principle 92

3.2 Straight-Line Solutions 98

3.3 Phase Portraits for Linear Systems with Real Eigenvalues 109

3.4 Complex Eigenvalues 120

3.5 Special Cases: Repeated and Zero Eigenvalues 127

3.6 Second-Order Linear Equations 136

3.7 The Trace-Determinant Plane 146

3.8 Linear Systems in Three Dimensions 150

Review Exercises 158

4 Forcing and Resonance 165

4.1 Forced Harmonic Oscillators 166

4.2 Sinusoidal Forcing 179

4.3 Undamped Forcing and Resonance 186

4.4 Amplitude and Phase of the Steady State 192

4.5 The Tacoma Narrows Bridge 194

Review Exercises 195

5 Nonlinear Systems 201

5.1 Equilibrium Point Analysis 202

5.2 Qualitative Analysis 215

5.3 Hamiltonian Systems 221

5.4 Dissipative Systems 225

5.5 Nonlinear Systems in Three Dimensions 232

5.6 Periodic Forcing of Nonlinear Systems and Chaos 234

Review Exercises 236

6 Laplace Transforms 245

6.1 Laplace Transforms 246

6.2 Discontinuous Functions 254

6.3 Second-Order Equations 260

6.4 Delta Functions and Impulse Forcing 270

6.5 Convolutions 272

6.6 The Qualitative Theory of Laplace Transforms 276

Review Exercises 277

7 Numerical Methods 285

7.1 Numerical Error in Euler's Method 286

7.2 Improving Euler's Method 296

7.3 The Runge-Kutta Method 300

7.4 The Effects of Finite Arithmetic 302

Review Exercises 302

8 Discrete Dynamical Systems 305

8.1 The Discrete Logistic Equation 306

8.2 Fixed Points and Periodic Points 308

8.3 Bifurcations 311

8.4 Chaos 313

Review Exercises 314

Appendices 317

A Changing Variables 318

B Power Series: The Ultimate Guess 328

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