This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
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34 of 38 people found the following review helpful:
5.0 out of 5 stars
Thorough and solid introduction,
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This review is from: Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics (Academic Press), 60.) (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
19 of 20 people found the following review helpful:
5.0 out of 5 stars
This is not a recipe book,
By
This review is from: Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics (Academic Press), 60.) (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.
6 of 6 people found the following review helpful:
4.0 out of 5 stars
A valuable source,
By maky m. (Miami FL) - See all my reviews
This review is from: Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics (Academic Press), 60.) (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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Inside This Book
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First Sentence:
The purpose of this short chapter is to develop some simple examples of differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
real canonical form, planar dynamical systems, nontrivial periodic solution, nonreal eigenvalues, nilpotent operator, hyperbolic flow, simple mechanical system, generalized eigenspaces, closed orbit, hyperbolic equilibrium, periodic attractor, dense open set, central force field, nilpotent matrix, solution curve, phase portrait, linear contraction, normed vector space, flow box, complex subspace Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Lemma Let, Jordan X-block New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
The purpose of this short chapter is to develop some simple examples of differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
real canonical form, planar dynamical systems, nontrivial periodic solution, nonreal eigenvalues, nilpotent operator, hyperbolic flow, simple mechanical system, generalized eigenspaces, closed orbit, hyperbolic equilibrium, periodic attractor, dense open set, central force field, nilpotent matrix, solution curve, phase portrait, linear contraction, normed vector space, flow box, complex subspace Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Lemma Let, Jordan X-block New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 13
books:
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6
books
cite this book:
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- Finite-Dimensional Vector Spaces by P.R. Halmos on page 208, and Back Matter
- Principles of Mechanics, 3rd Edition by John Synge on page 27, and Back Matter
- Calculus of Several Variables (Undergraduate Texts in Mathematics) by Serge Lang in Table of Contents, and Back Matter
- Ordinary Differential Equations (Classics in Applied Mathematics) by Philip Hartman in Back Matter
- Advanced Calculus, Revised Edition by Loomis in Back Matter
See all 13 books this book cites
- The Meaning of General Theoretical Sociology: Tradition and Formalization (American Sociological Association Rose Monographs) by Thomas J. Fararo in Back Matter
- Applied Differential Geometry by William L. Burke in Back Matter
- Individual Strategy and Social Structure: An Evolutionary Theory of Institutions by H. Peyton Young in Back Matter
- Nonlinear Dynamics, Mathematical Biology, And Social Science: Wise Use Of Alternative Therapies (Santa Fe Institute Series) by Joshua M. Epstein in Back Matter
- Encyclopedia of Mathematics Education by Louise Grinstein on page 540
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