Differential Equations

ISBN-10: 0495826723
ISBN-13: 9780495826729
Edition: 4th 2011
List price: $114.95
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Book details

List price: $114.95
Edition: 4th
Copyright year: 2011
Publisher: Brooks/Cole
Publication date: 5/18/2011
Binding: Paperback
Pages: 352
Size: 8.25" wide x 10.75" long x 0.75" tall
Weight: 3.674

Paul Blanchard has written Blue Guide Northern Italy and Blue Guide Southern Italy. Born in Amsterdam, New York, he has lived in Italy for more than thirty years.

Glen R. Hall is Associate Professor of Mathematics at Boston University. Glen spent most of his youth in Denver, Colorado. His undergraduate degree comes from Carleton College and his Ph.D. comes from the University of Minnesota. His research interests are mainly in low-dimensional dynamics and celestial mechanics. He has published numerous articles on the dynamics of circle and annulus maps. For his research he has been awarded both NSF Postdoctoral and Sloan Foundation Fellowships. He has no plans to open a CD store since he is busy raising his two young sons. He is an untalented, but earnest, trumpet player and golfer. He once bicycled 148 miles in a single day.

First-Order Differential Equations
Modeling via Differential Equations
Analytic Technique: Separation of Variables
Qualitative Technique: Slope Fields
Numerical Technique: Euler's Method
Existence and Uniqueness of Solutions
Equilibria and the Phase Line
Bifurcations
Linear Equations
Integrating Factors for Linear Equations
Review Exercises
First-Order Systems
Modeling via Systems
The Geometry of Systems
The Damped Harmonic Oscillator
Additional Analytic Methods for Special Systems
Euler's Method for Systems
Existence and Uniqueness for Systems
The SIR Model of an Epidemic
The Lorenz Equations
Review Exercises
Linear Systems
Properties of Linear Systems and The Linearity Principle
Straight-Line Solutions
Phase Portraits for Linear Systems with Real Eigenvalues
Complex Eigenvalues
Special Cases: Repeated and Zero Eigenvalues
Second-Order Linear Equations
The Trace-Determinant Plane
Linear Systems in Three Dimensions
Review Exercises
Forcing and Resonance
Forced Harmonic Oscillators
Sinusoidal Forcing
Undamped Forcing and Resonance
Amplitude and Phase of the Steady State
The Tacoma Narrows Bridge
Review Exercises
Nonlinear Systems
Equilibrium Point Analysis
Qualitative Analysis
Hamiltonian Systems
Dissipative Systems
Nonlinear Systems in Three Dimensions
Periodic Forcing of Nonlinear Systems and Chaos
Review Exercises
Laplace Transforms
Laplace Transforms
Discontinuous Functions
Second-Order Equations
Delta Functions and Impulse Forcing
Convolutions
The Qualitative Theory of Laplace Transforms
Review Exercises
Numerical Methods
Numerical Error in Euler's Method
Improving Euler's Method
The Runge-Kutta Method
The Effects of Finite Arithmetic
Review Exercises
Discrete Dynamical Systems
The Discrete Logistic Equation
Fixed Points and Periodic Points
Bifurcations
Chaos
Review Exercises
Appendices
Changing Variables
Power Series: The Ultimate Guess

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