9780495014614

Student Solutions Manual for Blanchard/Devaney/Hallís Differential Equations, 3rd

by ; ;
  • ISBN13:

    9780495014614

  • ISBN10:

    0495014613

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 3/17/2006
  • Publisher: Brooks Cole
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Summary

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

Table of Contents

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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