Advertisement

© 1991

Differential Equations: A Dynamical Systems Approach

Ordinary Differential Equations

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xx
  2. John H. Hubbard, Beverly H. West
    Pages 1-9
  3. John H. Hubbard, Beverly H. West
    Pages 11-65
  4. John H. Hubbard, Beverly H. West
    Pages 67-109
  5. John H. Hubbard, Beverly H. West
    Pages 111-156
  6. John H. Hubbard, Beverly H. West
    Pages 157-196
  7. John H. Hubbard, Beverly H. West
    Pages 197-295
  8. Back Matter
    Pages 297-350

About this book

Introduction

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.

Keywords

differential equation dynamical systems numerical method ordinary differential equation

Authors and affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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
  • Copyright Information Springer-Verlag New York 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-97286-2
  • Softcover ISBN 978-1-4612-6952-6
  • eBook ISBN 978-1-4612-0937-9
  • Series ISSN 0939-2475
  • Series E-ISSN 2196-9949
  • Edition Number 1
  • Number of Pages XX, 350
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
Industry Sectors
Aerospace
Finance, Business & Banking
IT & Software

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