Differential equations and dynamical systems
著者
書誌事項
Differential equations and dynamical systems
（Texts in applied mathematics, 7）
Springer-Verlag, c1991
- : us
- : gw
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387974439
内容説明
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 This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations. It is written for upper division or first-year graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations. An effi cient method for solving any linear system of ordinary differential equations is presented in Chapter 1."
- 巻冊次
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: gw ISBN 9783540974437
内容説明
This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behaviour of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated at the end of the 19th century. It is also intended as a reference book for mathematicians doing research on dynamical systems. There are several new features in this book such as the simplified proof of the HartmanGrobman Theorem and examples illustrating the proof, map in the theory of limit cycles, an efficient method for obtaining the global phase portrait of two-dimensional systems, and the description of the behaviour of a one-parameter family of limit cycles.
Readers of this book will find that, except for certain topics of current mathematical research such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system that rivals the understanding what we have of linear flows. This textbook on control/systems theory and ordinary differential equations is intended for mathematicians and physicists.
目次
Contents: Linear Systems.- Nonlinear Systems: Local Theory.- Nonlinear Systems: Global Theory.- Nonlinear Systems: Bifurcation Theory.
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