Differential Equations (with CD-ROM) 3rd Edition

30 customer reviews
ISBN-13: 978-0495012658
ISBN-10: 0495012653
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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. Integration Factors for Linear Equations. Review Exercises for Chapter 1. Labs for Chapter 1. 2. 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. 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. Review Exercises for Chapter 3. Labs for Chapter 3. 4. 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. 5. 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. 6. LAPLACE TRANSFORMS. Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Review Exercises for Chapter 6. Labs for Chapter 6. 7. 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. 8. 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. Hints and Answers. APPENDICES. Changing Variables. The Ultimate Guess. Complex Numbers and Euler's Formula.

About 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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Product Details

  • Hardcover: 828 pages
  • Publisher: Brooks Cole; 3 edition (September 19, 2005)
  • Language: English
  • ISBN-10: 0495012653
  • ISBN-13: 978-0495012658
  • Product Dimensions: 9.4 x 8 x 1.4 inches
  • Shipping Weight: 3.4 pounds
  • Average Customer Review: 3.3 out of 5 stars  See all reviews (30 customer reviews)
  • Amazon Best Sellers Rank: #512,984 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

6 of 7 people found the following review helpful By Leicester Dedlock on July 10, 2007
Format: Hardcover
Great for learning. Poor for reference.

This book is unique. Most differential equations textbooks simply provide formulae for different types of problems, but you don't really see the big picture. This book lets you see the big picture, but omits many of the most useful formulae that you may need in your career. This for that. It would be nice to see a book with the best of both worlds, but if you simply want to learn and understand the topic, this book is the way to go. Also, there is a good emphasis on qualitative and numerical techniques. Students often feel like they get less out of a mathematics class when qualitative and numerical techniques are emphasised over more analytic approaches. However, those of us who have worked in the "real world" know that the qualitative and numerical techniques are probably even more important. I have worked as a research statistician and my research areas emphasise computing. When I'm presented with real problems and real data (which, in my career, usually comes in large, unmanageable quantities), do I usually pull out my notebook and tackle the problem in a very precise manner, working out an exact solution? No, quite often I cannot realistically do that. Now I'll admit that I don't use much from this particular field on the job, but it still applies. Moving on, I must also mention that the book does a very good job at explaining these qualitative and numerical techniques in addition to things that are more analytic, although it is sometimes a little too verbose.

Regarding applications, the book covers a lot of fields and does put a big emphasis on applications. Physics, biology (especially population growth models), and electrical/computer engineering receive the most treatment.
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1 of 1 people found the following review helpful By P. Burnett on June 17, 2013
Format: Hardcover Verified Purchase
I bought this book with its accompanying CD as a companion to the superb DVD presentation on DE by one of its authors. "The Great Courses" video taught me lot more about DE than the courses I'd taken in the 50s and 60s. Wow! There's been a lot of progress in computer-based teaching as well as in mathematics. I simply wanted a hard-copy coupled with the capability to generate similar graphics on my laptop. The book plus CD provides that. So I'm very happy with the purchase.
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1 of 1 people found the following review helpful By mhartle on September 1, 2009
Format: Hardcover Verified Purchase
This book was very good at explaining all the situations I needed to cover. It provided detailed analysis of various problems that are applicable in every day life. The additional problems at the back of each chapter covered a wide range of difficulty levels and skills.
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2 of 3 people found the following review helpful By TherinOak on December 3, 2010
Format: Hardcover Verified Purchase
If you're buying this textbook because you'd like to learn differential equations, don't. The textbook isn't big on step by step explanations and there are few example cases and there's a lot of magical "and then this complicated equation becomes this simple one and we're assuming you can work that out!". It's annoying. The answer section in the back also does not have an explanations at all, just the answer.

I have a special view on this book though, because my professor who taught me Differential Equations, Robert Devaney, is one of the authors. The man is quite humorous, and so are his fellow authors, who frequently crack jokes in the book and questions at the end of the chapter. Differential Equations will make you smile. The only other good thing about this book is the software - some of it is very helpful in understanding the concepts and it is very easy to use.

Overall, if you don't need this textbook, don't buy it. If you do need this textbook, I swear you will only be using it to see what the homework problems are, so see if your library has a copy, or split the cost with a friend.
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2 of 3 people found the following review helpful By dudeth1 on November 1, 2010
Format: Hardcover Verified Purchase
As a college student, I don't really have a choice, nor do I normally care, what textbook is assigned for a certain class. For my entire math sequence from Calc I - Multivariable calculus I have used Stewart's Early Transcendentals and until I got this book for Differential, I never realized how well set up Stewart's Calculus textbook was. This differential book does not have clearly outlined example problems within the chapter that you can look at without reading through the text carefully. It was difficult to do the chapter homework problems without these easy to find examples to take you through it step by step. The derivation and life story of each equation is mostly irrelevant when it comes to passing an exam. I just want to know how to handle each problem and unique situation. Perhaps one should buy the solutions manual.
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2 of 3 people found the following review helpful By John on September 17, 2010
Format: Hardcover Verified Purchase
I had a relatively good experience with this book in the class that I used it for. Our professor was a real #%&$! and he wasn't that great at explaining the different concepts. I found myself coming back to this book countless times for clarification and help. Never let me down.

I'll admit that the format was a bit funky as far as introducing theorems and such, but overall, the problems were good for practicing and it was a life-saver for the final.
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By Josh Bartman on February 4, 2014
Format: Hardcover Verified Purchase
It's a required book for my class. It is pretty helpful.

The seller said it had no marks in it and it had the CD. It had marks in it and did not have the cd.

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