9780495826729

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

by ; ;
  • ISBN13:

    9780495826729

  • ISBN10:

    0495826723

  • Edition: 4th
  • Format: Paperback
  • Copyright: 5/18/2011
  • Publisher: Cengage Learning

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Summary

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

Table of Contents

First-Order Differential Equationsp. 1
Modeling via Differential Equationsp. 2
Analytic Technique: Separation of Variablesp. 6
Qualitative Technique: Slope Fieldsp. 16
Numerical Technique: Euler's Methodp. 20
Existence and Uniqueness of Solutionsp. 24
Equilibria and the Phase Linep. 27
Bifurcationsp. 33
Linear Equationsp. 38
Integrating Factors for Linear Equationsp. 46
Review Exercisesp. 55
First-Order Systemsp. 65
Modeling via Systemsp. 66
The Geometry of Systemsp. 68
The Damped Harmonic Oscillatorp. 74
Additional Analytic Methods for Special Systemsp. 77
Euler's Method for Systemsp. 80
Existence and Uniqueness for Systemsp. 82
The SIR Model of an Epidemicp. 84
The Lorenz Equationsp. 86
Review Exercisesp. 87
Linear Systemsp. 91
Properties of Linear Systems and The Linearity Principlep. 92
Straight-Line Solutionsp. 98
Phase Portraits for Linear Systems with Real Eigenvaluesp. 109
Complex Eigenvaluesp. 120
Special Cases: Repeated and Zero Eigenvaluesp. 127
Second-Order Linear Equationsp. 136
The Trace-Determinant Planep. 146
Linear Systems in Three Dimensionsp. 150
Review Exercisesp. 158
Forcing and Resonancep. 165
Forced Harmonic Oscillatorsp. 166
Sinusoidal Forcingp. 179
Undamped Forcing and Resonancep. 186
Amplitude and Phase of the Steady Statep. 192
The Tacoma Narrows Bridgep. 194
Review Exercisesp. 195
Nonlinear Systemsp. 201
Equilibrium Point Analysisp. 202
Qualitative Analysisp. 215
Hamiltonian Systemsp. 221
Dissipative Systemsp. 225
Nonlinear Systems in Three Dimensionsp. 232
Periodic Forcing of Nonlinear Systems and Chaosp. 234
Review Exercisesp. 236
Laplace Transformsp. 245
Laplace Transformsp. 246
Discontinuous Functionsp. 254
Second-Order Equationsp. 260
Delta Functions and Impulse Forcingp. 270
Convolutionsp. 272
The Qualitative Theory of Laplace Transformsp. 276
Review Exercisesp. 277
Numerical Methodsp. 285
Numerical Error in Euler's Methodp. 286
Improving Euler's Methodp. 296
The Runge-Kutta Methodp. 300
The Effects of Finite Arithmeticp. 302
Review Exercisesp. 302
Discrete Dynamical Systemsp. 305
The Discrete Logistic Equationp. 306
Fixed Points and Periodic Pointsp. 308
Bifurcationsp. 311
Chaosp. 313
Review Exercisesp. 314
Appendicesp. 317
Changing Variablesp. 318
Power Series: The Ultimate Guessp. 328
Table of Contents provided by Ingram. All Rights Reserved.

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