Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics (Academic Press), 60.)

8 customer reviews
ISBN-13: 978-0123495501
ISBN-10: 0123495504
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Product Details

  • Series: Pure and Applied Mathematics (Academic Press), 60. (Book 60)
  • Hardcover: 358 pages
  • Publisher: Academic Press (May 12, 1974)
  • Language: English
  • ISBN-10: 0123495504
  • ISBN-13: 978-0123495501
  • Product Dimensions: 1 x 6.8 x 9.5 inches
  • Shipping Weight: 1.6 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #416,697 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 26 people found the following review helpful By Vineet Gupta on September 15, 2003
Format: Hardcover
I can see that this is not the book for you if you want to solve a particular differential equation. But in terms of understanding the field of dynamical systems, there is no rival. This book is a pleasure to read, for the first time I understood the importance and beauty of linear algebra. Academic Press says that this is their most successful mathematics text, and it is not hard to see why. I wish more texts were as clearly written and as beautiful to read.
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39 of 44 people found the following review helpful By John S. Ryan on April 3, 2001
Format: Hardcover
This is the book from which I was introduced to dynamical systems some twenty-odd years ago. It's a thorough introduction that presumes a basic knowledge of multivariate differential calculus but is pretty well self-contained as far as linear algebra is concerned. Rigorous but readable, it provides a foundational understanding of n-dimensional linear dynamical systems and their basic exponential solution.

But my opinions won't be as helpful to the Amazon math shopper as a simple listing of what's in the book. So here's the table of contents.

Chapter 1: First Examples

Chapter 2: Newton's Equation and Kepler's Law

Chapter 3: Linear Systems with Constant Coefficiants and Real Eigenvalues

Chapter 4: Linear Systems with Constant Coefficients and Complex Eigenvalues

Chapter 5: Linear Systems and Exponentials of Operators

Chapter 6: Linear Systems and Canonical Forms of Operators

Chapter 7: Contractions and Generic Properties of Operators

Chapter 8: Fundamental Theory

Chapter 9: Stability of Equilibria

Chapter 10: Differential Equations for Electric Circuits

Chapter 11: The Poincare-Bendixson Theorem

Chapter 12: Ecology

Chapter 13: Periodic Attractors

Chapter 14: Classical Mechanics

Chapter 15: Nonautonomous Equations and Differentiability of Flows

Chapter 16: Perturbation Theory and Structural Stability

Afterword

Appendix I: Elementary Facts

Appendix II: Polynomials

Appendix III: On Canonical Forms

Appendix IV: The Inverse Function Theorem

References

Answers to Selected Problems
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8 of 8 people found the following review helpful By maky m. on June 10, 2005
Format: Hardcover
This book (the original version) has all the basics to introduce the future differential equations/dynamical systems researchers into the field. Written by authorities in the field (Hirsch and Smale,) this text offers a wide variety of topics, including linear systems, local and global stability theory for non-linear systems, and applications to physics and biology. As an added treat, the inclusion of basic linear algebra and operator theory makes this a rather self-contained work. The dedicated reader will not be disappointed - the material is well organised with sufficient level of detail, illustration, and exercises.
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3 of 3 people found the following review helpful By Carlos Frederico Trotta Matt on September 12, 2011
Format: Hardcover Verified Purchase
This is an excellent book with a rigorous mathematical treatment of differential equations. Important topics such as stability of dynamical systems and operator theory are covered in great detail. I recommend this book for an introductory graduate course on differential equations and dynamical systems.

Carlos Frederico Trotta Matt, Ph.D., Mechanical Engineer
Electric Power Research Center, Rio de Janeiro, Brazil
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