Differential Equations / Edition 2

Differential Equations / Edition 2

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

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ISBN-10: 0534385141

ISBN-13: 9780534385149

Pub. Date: 01/28/2002

Publisher: Brooks/Cole

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems

Overview

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.

Product Details

ISBN-13:
9780534385149
Publisher:
Brooks/Cole
Publication date:
01/28/2002
Edition description:
Older Edition
Pages:
816
Product dimensions:
8.16(w) x 9.52(h) x 1.38(d)

Table of Contents

1First-Order Differential Equations1
1.1Modeling via Differential Equations2
1.2Analytic Technique: Separation of Variables20
1.3Qualitative Technique: Slope Fields36
1.4Numerical Technique: Euler's Method53
1.5Existence and Uniqueness of Solutions65
1.6Equilibria and the Phase Line76
1.7Bifurcations96
1.8Linear Differential Equations113
1.9Changing Variables123
Labs for Chapter 1138
2First-Order Systems147
2.1Modeling via Systems148
2.2The Geometry of Systems165
2.3Analytic Methods for Special Systems183
2.4Euler's Method for Systems194
2.5The Lorenz Equations209
Labs for Chapter 2216
3Linear Systems225
3.1Properties of Linear Systems and the Linearity Principle226
3.2Straight-Line Solutions250
3.3Phase Planes for Linear Systems with Real Eigenvalues266
3.4Complex Eigenvalues282
3.5Special Cases: Repeated and Zero Eigenvalues301
3.6Second-Order Linear Equations316
3.7The Trace-Determinant Plane333
3.8Linear Systems in Three Dimensions346
Labs for Chapter 3362
4Forcing and Resonance369
4.1Forced Harmonic Oscillators370
4.2Sinusoidal Forcing385
4.3Undamped Forcing and Resonance397
4.4Amplitude and Phase of the Steady State409
4.5The Tacoma Narrows Bridge421
Labs for Chapter 4431
5Nonlinear Systems437
5.1Equilibrium Point Analysis438
5.2Qualitative Analysis457
5.3Hamiltonian Systems470
5.4Dissipative Systems488
5.5Nonlinear Systems in Three Dimensions510
5.6Periodic Forcing of Nonlinear Systems and Chaos518
Labs for Chapter 5535
6Laplace Transforms541
6.1Laplace Transforms542
6.2Discontinuous Functions554
6.3Second-Order Equations563
6.4Delta Functions and Impulse Forcing577
6.5Convolutions585
6.6The Qualitative Theory of Laplace Transforms594
Labs for Chapter 6603
7Numerical Methods607
7.1Numerical Error in Euler's Method608
7.2Improving Euler's Method621
7.3The Runge-Kutta Method629
7.4The Effects of Finite Arithmetic640
Labs for Chapter 7644
8Discrete Dynamical Systems647
8.1The Discrete Logistic Equation648
8.2Fixed Points and Periodic Points661
8.3Bifurcations670
8.4Chaos679
8.5Chaos in the Lorenz System687
Labs for Chapter 8693
Appendices699
AFirst-Order Linear Equations Revisited700
BComplex Numbers and Euler's Formula711
Hints and Answers717
Index777

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