Differential Equations (with DE Tools Printed Access Card) / Edition 4

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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.
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Product Details

  • ISBN-13: 9781133109037
  • Publisher: Cengage Learning
  • Publication date: 4/11/2011
  • Edition description: New Edition
  • Edition number: 4
  • Pages: 864
  • Sales rank: 195,094
  • Product dimensions: 8.30 (w) x 9.40 (h) x 1.50 (d)

Meet the Author


Paul Blanchard is Associate Professor of Mathematics at Boston University. Paul grew up in Sutton, Massachusetts, spent his undergraduate years at Brown University, and received his Ph.D. from Yale University. He has taught college mathematics for twenty-five years, mostly at Boston University. In 2001, he won the Northeast Section of the Mathematical Association of America's Award for Distinguished Teaching in Mathematics. He has coauthored or contributed chapters to four different textbooks. His main area of mathematical research is complex analytic dynamical systems and the related point sets, Julia sets and the Mandelbrot set. Most recently his efforts have focused on reforming the traditional differential equations course, and he is currently heading the Boston University Differential Equations Project and leading workshops in this innovative approach to teaching differential equations. When he becomes exhausted fixing the errors made by his two coauthors, he usually closes up his CD store and heads to the golf course with his caddy, Glen Hall.

Robert L. Devaney is Professor of Mathematics at Boston University. Robert was raised in Methuen, Massachusetts. He received his undergraduate degree from Holy Cross College and his Ph.D. from the University of California, Berkeley. He has taught at Boston University since 1980. His main area of research is complex dynamical systems, and he has lectured extensively throughout the world on this topic. In 1996 he received the National Excellence in Teaching Award from the Mathematical Association of America. When he gets sick of arguing with his coauthors over which topics to include in the differential equations course, he either turns up the volume of his opera CDs, or heads for waters off New England for a long distance sail.

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.

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Table of Contents


1. 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. 2. FIRST-ORDER SYSTEMS. Modeling via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. The Lorenz Equations. 3. 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. 4. FORCING AND RESONANCE. Forced Harmonic Oscillators. Sinusoidal Forcing. Undamped Forcing and Resonance. Amplitude and Phase of the Steady State. The Tacoma Narrows Bridge. 5. NONLINEAR SYSTEMS. Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Periodic Forcing of Nonlinear Systems and Chaos. 6. LAPLACE TRANSFORMS. Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. 7. NUMERICAL METHODS. Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. 8. DISCRETE DYNAMICAL SYSTEMS. The Discrete Logistic Equation. Fixed Points and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. APPENDICES. A. Changing Variables. B. The Ultimate Guess. C. Complex Numbers and Euler's Formula.
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Customer Reviews

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Sort by: Showing all of 4 Customer Reviews
  • Anonymous

    Posted September 4, 2012

    Read Me Like a Novel

    I hate this math book. Don't get me wrong! It taught the material, but it wanted to be read like a book which made it rather confusing and hard to understand/find examples of what you were suppose to be doing.

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  • Anonymous

    Posted May 22, 2002

    Try Something else

    I used this course in a differential equations course and found it disorganized and confusing. An entire section was built on the notion of 'guessing' solutions -- this was completely unnecessary as subsequent sections showed how to avoid the guessing process in solving ordinary d.e. Overall, there must be better introductions to this interesting subject.

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  • Anonymous

    Posted November 30, 2001

    Effective introduction

    The prose was uniformly easy to follow and not at all stilted. The presentation was generally clear but I agree with others that the pace was sometimes too slow and sometimes slightly too fast. The appendix included enough background on prerequisite topics like the complex exponential to make the book accessible to anyone with a good foundation in calculus. I personally did well in my course and feel I owe that success, in large part, to this book.

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  • Anonymous

    Posted August 21, 2001

    Best Introductory ODE Book Available!

    Nothing but good things to say about the book... written in a very reader friendly style without losing any necessary mathematical rigor.

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