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Differential Equations

ISBN-10: 0495012653
ISBN-13: 9780495012658
Edition: 3rd 2006 (Revised)
List price: $316.95
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Description: Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of  More...

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Book details

List price: $316.95
Edition: 3rd
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 9/19/2005
Binding: Mixed Media
Pages: 848
Size: 8.00" wide x 9.00" long x 1.50" tall
Weight: 3.696
Language: English

Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.

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 for Chapter 1
Labs for Chapter 1
First-Order Systems
Modeling via Systems
The Geometry of Systems
Analytic Methods for Special Systems
Euler's Method for Systems
The Lorenz Equations
Review Exercises for Chapter 2
Labs for Chapter 2
Linear Systems
Properties of Linear Systems and the Linearity Principle
Straight-Line Solutions
Phase Planes 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 for Chapter 3
Labs for Chapter 3
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 for Chapter 4
Labs for Chapter 4
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 for Chapter 5
Labs for Chapter 5
Laplace Transforms
Laplace Transforms
Discontinuous Functions
Second-Order Equations
Delta Functions and Impulse Forcing
Convolutions
The Qualitative Theory of Laplace Transforms
Table of Laplace Transforms
Review Exercises for Chapter 6
Labs for Chapter 6
Numerical Methods
Numerical Error in Euler's Method
Improving Euler's Method
The Runge-Kutta Method
The Effects of Finite Arithmetic
Review Exercises for Chapter 7
Labs for Chapter 7
Discrete Dynamical Systems
The Discrete Logistic Equation
Fixed Points and Periodic Points
Bifurcations
Chaos
Chaos in the Lorenz System
Review Exercises for Chapter 8
Labs for Chapter 8
Appendices
Changing Variables
The Ultimate Guess
Complex Numbers and Euler's Formula
Hints and Answers
Index

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