Ordinary differential equations
著者
書誌事項
Ordinary differential equations
（Texts in applied mathematics, 5 . Differential equations : a dynamical systems approach ; pt. 1）
Springer-Verlag, c1991
- : New York
- : Berlin
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注記
Includes bibliographical references (p. [307]-308) and index
The description of the title is on the t.p. only
内容説明・目次
- 巻冊次
-
: New York ISBN 9780387972862
内容説明
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.
目次
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
- 巻冊次
-
: Berlin ISBN 9783540972860
内容説明
This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book 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. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.
目次
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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