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

, by Blanchard, Paul; Devaney, Robert; Hall, Glen

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ISBN: 9780495826729 | 0495826723
Cover: Paperback
Copyright: 5/18/2011

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Summary

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

First-Order Differential Equations	p. 1
Modeling via Differential Equations	p. 2
Analytic Technique: Separation of Variables	p. 6
Qualitative Technique: Slope Fields	p. 16
Numerical Technique: Euler's Method	p. 20
Existence and Uniqueness of Solutions	p. 24
Equilibria and the Phase Line	p. 27
Bifurcations	p. 33
Linear Equations	p. 38
Integrating Factors for Linear Equations	p. 46
Review Exercises	p. 55
First-Order Systems	p. 65
Modeling via Systems	p. 66
The Geometry of Systems	p. 68
The Damped Harmonic Oscillator	p. 74
Additional Analytic Methods for Special Systems	p. 77
Euler's Method for Systems	p. 80
Existence and Uniqueness for Systems	p. 82
The SIR Model of an Epidemic	p. 84
The Lorenz Equations	p. 86
Review Exercises	p. 87
Linear Systems	p. 91
Properties of Linear Systems and The Linearity Principle	p. 92
Straight-Line Solutions	p. 98
Phase Portraits for Linear Systems with Real Eigenvalues	p. 109
Complex Eigenvalues	p. 120
Special Cases: Repeated and Zero Eigenvalues	p. 127
Second-Order Linear Equations	p. 136
The Trace-Determinant Plane	p. 146
Linear Systems in Three Dimensions	p. 150
Review Exercises	p. 158
Forcing and Resonance	p. 165
Forced Harmonic Oscillators	p. 166
Sinusoidal Forcing	p. 179
Undamped Forcing and Resonance	p. 186
Amplitude and Phase of the Steady State	p. 192
The Tacoma Narrows Bridge	p. 194
Review Exercises	p. 195
Nonlinear Systems	p. 201
Equilibrium Point Analysis	p. 202
Qualitative Analysis	p. 215
Hamiltonian Systems	p. 221
Dissipative Systems	p. 225
Nonlinear Systems in Three Dimensions	p. 232
Periodic Forcing of Nonlinear Systems and Chaos	p. 234
Review Exercises	p. 236
Laplace Transforms	p. 245
Laplace Transforms	p. 246
Discontinuous Functions	p. 254
Second-Order Equations	p. 260
Delta Functions and Impulse Forcing	p. 270
Convolutions	p. 272
The Qualitative Theory of Laplace Transforms	p. 276
Review Exercises	p. 277
Numerical Methods	p. 285
Numerical Error in Euler's Method	p. 286
Improving Euler's Method	p. 296
The Runge-Kutta Method	p. 300
The Effects of Finite Arithmetic	p. 302
Review Exercises	p. 302
Discrete Dynamical Systems	p. 305
The Discrete Logistic Equation	p. 306
Fixed Points and Periodic Points	p. 308
Bifurcations	p. 311
Chaos	p. 313
Review Exercises	p. 314
Appendices	p. 317
Changing Variables	p. 318
Power Series: The Ultimate Guess	p. 328
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Student Solutions Manual for Blanchard/Devaney/Hall's Differential Equations, 4th

Summary

Table of Contents

Supplemental Materials