Differential Equations: A Dynamical Systems Approach: Ordinary Differential Equations / Edition 1

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Overview

This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

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Editorial Reviews

From the Publisher
.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

Booknews
Textbook for an advanced undergraduate course (e.g. in applicable mathematics) shows students the solutions to a differential equation and how they behave, by using computer graphics and numerical methods to produce pictures for qualitative study. A companion software package for the Macintosh called MacMath is referred to throughout, though other programs may be substituted. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387972862
  • Publisher: Springer New York
  • Publication date: 2/4/1991
  • Series: Texts in Applied Mathematics Series , #5
  • Edition description: 1st ed. 1991. Corr. 3rd printing 1997
  • Edition number: 1
  • Pages: 395
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.94 (d)

Table of Contents

Contents Series Preface for Texts in Applied Mathematics Preface Acknowledgments Ways to Use This Book Introduction Chapter 1 Qualitative Methods 1.1 Fields of Slopes and Sketching of Solutions 1.2 Qualitative Description of Solutions 1.3 Fences 1.4 Funnels and Antifunnels 1.5 The Use of Fences, Funnels, and Antifunnels Exercises Chapter 2 Analystic Methods 2.1 Separation of Variables 2.2 Linear Differential Equations of First Order 2.3 Variation of Parameters 2.4 Bank Accounts and Linear Differential Equations

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