This book is about the study of systems of differential equations (DEs), or more precisely, systems of 1st-order ordinary differential equations. As we shall see, any higher-order system of differential equations can be reduced to a 1st-order system and thus the study of first-order systems suffices for the general theory. Many systems of differential equations model the motion of something, and for this reason systems of DEs are often referred to as dynamical systems.
The purpose of this introduction is not only to present a number of examples which serve to illustrate the main concepts and ideas involved in the study of dynamical systems, but also to give some of the initial mathematical definitions for these concepts. Do not be concerned with the complexity of some of these examples or the physics behind them. For now, just read and get an overview of what dynamical systems are (if you do not already have experience with them from elsewhere).
KeywordsNormal Form Phase Portrait Stagnation Point Autonomous System Integral Curve
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