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Rating: 
Summary: Not for the average undergrad!
Review: As a senior undergrad majoring in math and economics, this book is everything but an easy read. To all fellow undergrads who are not math superheroes (that should about 75% of us), if you happen to come across this book in an upcoming course description, it may be a good idea to look for alternative. Currently, I'm looking for another book that I may be able to use as a supplement to get me through this course with a passing grade. Up to this point in my math career, I have never come across a text as ungraspable as this one; this is unfortunate since it appears that there is a lot of knowledge and content on the pages.
Rating: 
Summary: This is not a recipe book
Review: 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.
Rating:
Summary: This is not a recipe book
Review: 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.
Rating: 
Summary: A complete waste
Review: This is not a book, it's a piece of trash!!! This so called book is a meaningless mess which wasn't even understandable for the person who had a PhD in math and was teaching our class. Do NOT bother with this nonsense. if you want to learn something just read Ordinary Differential Equations by V. I. Arnold.I would have given no star if I could!!!Just go with Arnold's and I'll be WAY better off.
Rating:
Summary: Thorough and solid introduction
Review: 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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