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Differential Equations: A Dynamical Systems Approach

Ordinary Differential Equations

  • Textbook
  • © 1991

Overview

Authors:
  1. John H. Hubbard

    1. Department of Mathematics, Cornell University, Ithaca, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Beverly H. West

    1. Department of Mathematics, Cornell University, Ithaca, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts in Applied Mathematics (TAM, volume 5)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Introduction

    • John H. Hubbard, Beverly H. West
    Pages 1-9

  3. Qualitative Methods

    • John H. Hubbard, Beverly H. West
    Pages 11-65

  4. Analytic Methods

    • John H. Hubbard, Beverly H. West
    Pages 67-109

  5. Numerical Methods

    • John H. Hubbard, Beverly H. West
    Pages 111-156

  6. Fundamental Inequality, Existence, and Uniqueness

    • John H. Hubbard, Beverly H. West
    Pages 157-196

  7. Iteration

    • John H. Hubbard, Beverly H. West
    Pages 197-295

  8. Back Matter

    Pages 297-350
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Keywords

About this book

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM) . The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface Consider a first order differential equation of form x' = f ( t, x). In elemen­ tary courses one frequently gets the impression that such equations can usually be "solved," i. e. , that explicit formulas for the solutions (in terms of powers, exponentials, trigonometric functions, and the like) can usually be found. Nothing could be further from the truth.

Reviews

.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

Authors and Affiliations

  • Department of Mathematics, Cornell University, Ithaca, USA

    John H. Hubbard, Beverly H. West

Bibliographic Information

  • Book Title: Differential Equations: A Dynamical Systems Approach

  • Book Subtitle: Ordinary Differential Equations

  • Authors: John H. Hubbard, Beverly H. West

  • Series Title: Texts in Applied Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0937-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Hardcover ISBN: 978-0-387-97286-2Published: 04 February 1991

  • Softcover ISBN: 978-1-4612-6952-6Published: 19 November 2013

  • eBook ISBN: 978-1-4612-0937-9Published: 27 November 2013

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 1

  • Number of Pages: XX, 350

  • Topics: Analysis

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