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.

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

This book is a classical in the subject. It will provide you with solid information even if you are an absolut beginner with proficiency only in undergraduate algebra, calculus.

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