Differential Equations and Dynamical Systems

1. Front Matter

   Pages i-xii

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2. Linear Systems

   • Lawrence Perko

   Pages 1-63

3. Nonlinear Systems: Local Theory

   • Lawrence Perko

   Pages 65-161

4. Nonlinear Systems: Global Theory

   • Lawrence Perko

   Pages 163-290

5. Nonlinear Systems: Bifurcation Theory

   • Lawrence Perko

   Pages 291-393

6. Back Matter

   Pages 395-403

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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 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.

• Dynamical system
• Eigenvalue
• differential equation
• maximum
• ordinary differential equation

• Department of Mathematics, Northern Arizona University, Flagstaff, USA

  Lawrence Perko

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