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Mathematics - Analysis | Differential Equations: A Dynamical Systems Approach - Ordinary Differential Equations

Differential Equations: A Dynamical Systems Approach

Ordinary Differential Equations

Series: Texts in Applied Mathematics, Vol. 5

Volume package: Differential Equations

Hubbard, John H., West, Beverly H.

1991, XX, 350 p.

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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.

Content Level » Graduate

Keywords » differential equation - dynamical systems - numerical method - ordinary differential equation

Related subjects » Analysis

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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