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Differential Equations

ISBN-10: 0534385141
ISBN-13: 9780534385149
Edition: 2nd 2002
List price: $165.95
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Description: 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  More...

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Book details

List price: $165.95
Edition: 2nd
Copyright year: 2002
Publisher: Brooks/Cole
Publication date: 1/18/2002
Binding: Hardcover
Pages: 816
Size: 8.00" wide x 9.25" long x 1.25" tall
Weight: 3.190
Language: English

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.

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 Equationsp. 1
Modeling via Differential Equationsp. 2
Analytic Technique: Separation of Variablesp. 20
Qualitative Technique: Slope Fieldsp. 36
Numerical Technique: Euler's Methodp. 53
Existence and Uniqueness of Solutionsp. 65
Equilibria and the Phase Linep. 76
Bifurcationsp. 96
Linear Differential Equationsp. 113
Changing Variablesp. 123
Labs for Chapter 1p. 138
First-Order Systemsp. 147
Modeling via Systemsp. 148
The Geometry of Systemsp. 165
Analytic Methods for Special Systemsp. 183
Euler's Method for Systemsp. 194
The Lorenz Equationsp. 209
Labs for Chapter 2p. 216
Linear Systemsp. 225
Properties of Linear Systems and the Linearity Principlep. 226
Straight-Line Solutionsp. 250
Phase Planes for Linear Systems with Real Eigenvaluesp. 266
Complex Eigenvaluesp. 282
Special Cases: Repeated and Zero Eigenvaluesp. 301
Second-Order Linear Equationsp. 316
The Trace-Determinant Planep. 333
Linear Systems in Three Dimensionsp. 346
Labs for Chapter 3p. 362
Forcing and Resonancep. 369
Forced Harmonic Oscillatorsp. 370
Sinusoidal Forcingp. 385
Undamped Forcing and Resonancep. 397
Amplitude and Phase of the Steady Statep. 409
The Tacoma Narrows Bridgep. 421
Labs for Chapter 4p. 431
Nonlinear Systemsp. 437
Equilibrium Point Analysisp. 438
Qualitative Analysisp. 457
Hamiltonian Systemsp. 470
Dissipative Systemsp. 488
Nonlinear Systems in Three Dimensionsp. 510
Periodic Forcing of Nonlinear Systems and Chaosp. 518
Labs for Chapter 5p. 535
Laplace Transformsp. 541
Laplace Transformsp. 542
Discontinuous Functionsp. 554
Second-Order Equationsp. 563
Delta Functions and Impulse Forcingp. 577
Convolutionsp. 585
The Qualitative Theory of Laplace Transformsp. 594
Labs for Chapter 6p. 603
Numerical Methodsp. 607
Numerical Error in Euler's Methodp. 608
Improving Euler's Methodp. 621
The Runge-Kutta Methodp. 629
The Effects of Finite Arithmeticp. 640
Labs for Chapter 7p. 644
Discrete Dynamical Systemsp. 647
The Discrete Logistic Equationp. 648
Fixed Points and Periodic Pointsp. 661
Bifurcationsp. 670
Chaosp. 679
Chaos in the Lorenz Systemp. 687
Labs for Chapter 8p. 693
Appendicesp. 699
First-Order Linear Equations Revisitedp. 700
Complex Numbers and Euler's Formulap. 711
Hints and Answersp. 717
Indexp. 777
Table of Contents provided by Syndetics. All Rights Reserved.

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