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

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

• ISBN13: 9780495014614
• ISBN10: 0495014613
• Edition: 3rd
• Format: Paperback
• Copyright: 2006-03-17
• Publisher: Brooks Cole

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