Differential Equations (with CD-ROM)

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

• ISBN13: 9780534385149
• ISBN10: 0534385141
• Edition: CD
• Format: Hardcover
• Copyright: 2002-01-18
• Publisher: Brooks Cole

Summary

The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation.

Table of Contents

First-Order Differential Equations	1	(146)
Modeling via Differential Equations	2	(18)
Analytic Technique: Separation of Variables	20	(16)
Qualitative Technique: Slope Fields	36	(17)
Numerical Technique: Euler's Method	53	(12)
Existence and Uniqueness of Solutions	65	(11)
Equilibria and the Phase Line	76	(20)
Bifurcations	96	(17)
Linear Differential Equations	113	(10)
Changing Variables	123	(24)
Labs for Chapter 1	138	(9)
First-Order Systems	147	(78)
Modeling via Systems	148	(17)
The Geometry of Systems	165	(18)
Analytic Methods for Special Systems	183	(11)
Euler's Method for Systems	194	(15)
The Lorenz Equations	209	(16)
Labs for Chapter 2	216	(9)
Linear Systems	225	(144)
Properties of Linear Systems and the Linearity Principle	226	(24)
Straight-Line Solutions	250	(16)
Phase Planes for Linear Systems with Real Eigenvalues	266	(16)
Complex Eigenvalues	282	(19)
Special Cases: Repeated and Zero Eigenvalues	301	(15)
Second-Order Linear Equations	316	(17)
The Trace-Determinant Plane	333	(13)
Linear Systems in Three Dimensions	346	(23)
Labs for Chapter 3	362	(7)
Forcing and Resonance	369	(68)
Forced Harmonic Oscillators	370	(15)
Sinusoidal Forcing	385	(12)
Undamped Forcing and Resonance	397	(12)
Amplitude and Phase of the Steady State	409	(12)
The Tacoma Narrows Bridge	421	(16)
Labs for Chapter 4	431	(6)
Nonlinear Systems	437	(104)
Equilibrium Point Analysis	438	(19)
Qualitative Analysis	457	(13)
Hamiltonian Systems	470	(18)
Dissipative Systems	488	(22)
Nonlinear Systems in Three Dimensions	510	(8)
Periodic Forcing of Nonlinear Systems and Chaos	518	(23)
Labs for Chapter 5	535	(6)
Laplace Transforms	541	(66)
Laplace Transforms	542	(12)
Discontinuous Functions	554	(9)
Second-Order Equations	563	(14)
Delta Functions and Impulse Forcing	577	(8)
Convolutions	585	(9)
The Qualitative Theory of Laplace Transforms	594	(13)
Labs for Chapter 6	603	(4)
Numerical Methods	607	(40)
Numerical Error in Euler's Method	608	(13)
Improving Euler's Method	621	(8)
The Runge-Kutta Method	629	(11)
The Effects of Finite Arithmetic	640	(7)
Labs for Chapter 7	644	(3)
Discrete Dynamical Systems	647	(52)
The Discrete Logistic Equation	648	(13)
Fixed Points and Periodic Points	661	(9)
Bifurcations	670	(9)
Chaos	679	(8)
Chaos in the Lorenz System	687	(12)
Labs for Chapter 8	693	(6)
APPENDICES	699	(18)
A First-Order Linear Equations Revisited	700	(11)
B Complex Numbers and Euler's Formula	711	(6)
Hints and Answers	717	(60)
Index	777