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. Customer Book Reviews This is not a recipe book By Vineet Gupta on Sep 15, 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.

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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. Customer Book Reviews This is not a recipe book By Vineet Gupta on Sep 15, 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. Thorough and solid introduction By John S. Ryan on Apr 03, This is the book from which I was introduced to dynamical systems some twenty-odd years ago. Rigorous but readable, it provides a foundational understanding of n-dimensional linear dynamical systems and their basic exponential solution. 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.

Differential equations, dynamical systems and linear algebra By Carlos Frederico Trotta Matt on Sep 12, 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. It will provide you with solid information even if you are an absolut beginner with proficiency only in undergraduate algebra, calculus. Not for the average undergrad! By Krauss99 on Jan 30, As a senior undergrad majoring in math and economics, this book is everything but an easy read. 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.

Do NOT bother with this nonsense. I would have given no star if I could!!! Serious Business By Neil Delaney on Apr 23, We used this text in the second quarter of my frosh honors calculus class in college back in I found it very difficult. Schoenagel on Jan 15, The Preface: "this book can be used as early as the sophomore year" and "Our goal is to develop nonlinear ordinary differential equations in open subsets of real Cartesian space in such a way that extension to manifolds is simple and natural.

Look at the Problems! And, as is evident before one proceeds too far, the "chain rule" will be utilized over and over again. Theorem Two is the capstone of the chapter: "By using this theorem we get much information about the general solutions directly from knowledge of the eigenvalues, without solving the differential equation.

Now, before continuing with the text, re-read the first three chapters. Do every problem or, at the least re-do every example. This will be a short interlude of ten pages. Here you will get a survey of introductory Topology. Norms and Operators, follow. Take note of: The correspondence, page 85, between complex numbers and 2X2 matrices. By the way, only square matrices are utilized in the text. Also, the series expansion of exponential and trigonometric functions should be second-nature.

Homogeneous,then, nonhomogeneous equations. Autonomous no explicit time-dependence followed by nonautonomous page Take-away: Variation of Parameters. Another clue: Liebniz.

And, read: "The eigenvector theory of real linear operator is rarely treated in texts, and is important for theory of linear differential equations. Read: "Operators on function spaces have many uses for both theoretical and practical work in differential equations. Equilibrium states, defined. Glance at Problem 4 page Surely, many physics students have been exposed previously to this equation. Now, it is placed into mathematical context.

Learn the meaning of "dense" page , and Problem 1, page If you are unfamiliar with things such as Lipschitz condition or, manipulating epsilons and deltas , then, a review of such is recommended.

Uniform Convergence, too, should be firmly grasped. Or, glance at Problems 1,4, and 5, page Serge Lang, again, is prime reference. We continue with Stability and Equilibria: Glance at the example of page , graph--by hand-- this multivariable function. True, it is easier if you use a computer for that Maple, Mathematica, etc. By the way, terms such as kinetic energy, potential energy, and conservative forces should already be firmly grasped.

See: Symon. Theory, again, in Chapter Thirteen fear not, glance at Problem 1, page , that is not difficult. That is, perturbations. The authors write: "this book is only an introduction to the subject of dynamical systems" and "Appendix One elementary facts should have been seen before" And, if you are searching for "manifolds" turn elsewhere Arnold. Now, my concluding thoughts regarding the book: This is not such a terrible book.

Here we have three topics--differential equations and dynamical systems and linear algebra. As usual, you run the risk of pleasing no one when you attempt to please everyone.

Any one of those topics can fill an entire book. Here, in span of pages, we are exposed to all three topics. And, to make matters more involved, if said student is unaccustomed to mathematical proofs at sophomore level , then much in the later chapters will be difficult to follow.

One makes comparison to the beautiful textbooks of Hubbard and West, they write of Hirsch and Smale: " this is the first book bringing modern developments of differential equations to a broad audience " and "Smale has profoundly influenced the authors.

As with their recommendation of the text, I do the same. My first course in Differential Equations left me with a potpourri of "tricks" and computer graphics, as but memories. This text will hopefully instill less of that "trickery" with more mathematical connections and more understanding. Hirsch , Stephen Smale. This particular edition is in a Hardcover format. It was published by Academic Press and has a total of pages in the book. To buy this book at the lowest price, Click Here. Similar Books.

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## Differential Equations, Dynamical Systems, and Linear Algebra

Personal information is secured with SSL technology. Free Shipping No minimum order. Description 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. Readership Advanced undergraduate and graduate students studying mathematics.

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## Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics)

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