Ebook: Differential Equations: A Dynamical Systems Approach: Higher-Dimensional Systems

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, had 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 Math­ ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface As in Part I, this book concentrates on understanding the behavior of dif­ ferential equations, rather than on solving the equations. Part I focused on differential equations in one dimension; this volume attempts to understand differential equations in n dimensions. The existence and uniqueness theory carries over with almost no changes.

---

This book is the second part of the text DifferentialEquations: A Dynamical Systems Approach written by John Hubbard and Beverly West. It is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations. This book will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, applied mathematics, as well as in the life sciences, physics, and economics.
This book opens with an introduction, and follows with chapters on systems of differential equations, systems of linear differential equations, and systems of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The authors also include an appendix containing important theorems from parts I and II, as well as answers to selected problems.

---

This book is the second part of the text DifferentialEquations: A Dynamical Systems Approach written by John Hubbard and Beverly West. It is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations. This book will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, applied mathematics, as well as in the life sciences, physics, and economics.
This book opens with an introduction, and follows with chapters on systems of differential equations, systems of linear differential equations, and systems of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The authors also include an appendix containing important theorems from parts I and II, as well as answers to selected problems.
Content:
Front Matter....Pages i-xiv
Systems of Differential Equations....Pages 1-68
Systems of Differential Equations....Pages 69-129
Systems of Nonlinear Differential Equations....Pages 131-201
Structural Stability....Pages 203-264
Bifurcations....Pages 265-368
Back Matter....Pages 369-602

---

This book is the second part of the text DifferentialEquations: A Dynamical Systems Approach written by John Hubbard and Beverly West. It is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations. This book will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, applied mathematics, as well as in the life sciences, physics, and economics.
This book opens with an introduction, and follows with chapters on systems of differential equations, systems of linear differential equations, and systems of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The authors also include an appendix containing important theorems from parts I and II, as well as answers to selected problems.
Content:
Front Matter....Pages i-xiv
Systems of Differential Equations....Pages 1-68
Systems of Differential Equations....Pages 69-129
Systems of Nonlinear Differential Equations....Pages 131-201
Structural Stability....Pages 203-264
Bifurcations....Pages 265-368
Back Matter....Pages 369-602
....