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Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems (Texts in Applied Mathematics) (Pt. 2)
 
 
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Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems (Texts in Applied Mathematics) (Pt. 2) [Hardcover]

John H. Hubbard (Author), Beverly H. West (Author)
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

0387943773 978-0387943770 March 30, 1995 1
This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics.
After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.

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Customers buy this book with Differential Equations and Their Applications : An Introduction to Applied Mathematics (Texts in Applied Mathematics, Vol. 11) $52.94

Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems (Texts in Applied Mathematics) (Pt. 2) + Differential Equations and Their Applications : An Introduction to Applied Mathematics (Texts in Applied Mathematics, Vol. 11)
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Editorial Reviews

Review

.H. Hubbard and B.H. West

Differential Equations: A Dynamical Systems Approach

"As attention has moved from idealized linear differential equations to the nonlinear equations of the real world, there has been a concomitant change of emphasis, even a paradigm shift, from quantitative methods, analytical and numerical, to qualitative methods. Though qualitative methods originated with Poincaré (Poincare) early in this century, the era of large-scale computation and computer graphics has spurred development through a profound confluence of theory and experiment. Hubbard and West demonstrate convincingly that it is feasible and necessary to incorporate this sophisticated viewpoint into the most elementary stages of differential equations pedagogy, even where the focus is still on linear equations. This is an unusual book in being both rigorous and squarely addressed to those students with the most practical needs. The well known exchange value between pictures and words is thoroughly exploited to ground fundamental concepts."—CHOICE

--This text refers to an alternate Hardcover edition.

Product Details

  • Hardcover: 615 pages
  • Publisher: Springer; 1 edition (March 30, 1995)
  • Language: English
  • ISBN-10: 0387943773
  • ISBN-13: 978-0387943770
  • Product Dimensions: 9.3 x 6.2 x 1.4 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,234,269 in Books (See Top 100 in Books)

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8 of 9 people found the following review helpful:
5.0 out of 5 stars Unusually Excellent book on Diff-Eq, September 23, 2005
The vast majority of books on differential equations (at any level--introductory or advanced) are absolute garbage. This book is a true exception.

Easy to read, extraordinarily compact, very deep. This book is suitable for anyone attempting to learn differential equations: it has a lot of very useful and well-written explanatory text, and it paints an overall picture of the subject in addition to teaching specific techniques and giving the reader a good sense of which techniques are useful in which situations.

It assumes very little background (basic calculus) but gets into some very advanced material fairly quickly. Don't waste your time with the typical big undergrad diffeq books--get one like this: you will not regret it!
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5 of 18 people found the following review helpful:
5.0 out of 5 stars Excellent book!, October 29, 1999
By A Customer
This review is from: Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems (Texts in Applied Mathematics) (Pt. 2) (Hardcover)
Very clear and intuitive upper-undergrad/graduate level text. I highly recomend it.
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Inside This Book (learn more)
First Sentence:
In many (in fact, most) cases, differential equations of the form x' = f(t, x) are inadequate for the description of a physical system; more variables are needed to specify its state at any time t. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
homoclinic saddle connection, heteroclinic saddle connection, repelling limit cycles, stable separatrix, degenerate possibility, differentiable conjugacy, unstable separatrices, saddle connections, weak sink, spiral sink, phase plane behavior, bifurcation locus, essential size, linear sink, distinct absolute values, exceptional trajectory, many limit cycles, spiral source, linearization matrix, upper fence, node sink, two limit cycles, exceptional solution, associated homogeneous equation, degenerate bifurcations
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Selected Problems, Implicit Function Theorem, Spectral Theorem, Exercises Exercises, Consider Example, Higher Order Equations, Kepler's First Law, Planar Systems, Repeat Exercise, Asymptotic Development, Bifurcations of Vector Fields, Inverse Function Theorem, Schwarz Inequality
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