Customer Reviews

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

5 star:		(4)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

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

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.

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.

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

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.

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 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.