Scheinerman E.R.  Invitation to dynamical systems

Название: 
Invitation to dynamical systems 
Автор: 
Scheinerman E.R. 
Категория: 
Математика

Тип: 
Книга 
Дата: 
30.12.2008 23:35:21 
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Описание: 
Popular treatments of chaos, fractals, and dynamical systems let the public ] know there is a party but provide no map to the festivities. Advanced texts e assume their readers are already part of the club. This Invitation, however, c is meant to attract a wider audience; I hope to attract my guests to the beauty and excitement of dynamical systems in particular and of mathematics in general.
For this reason the technical prerequisites for this book are modest. F Students need to have studied two semesters of calculus and one semester 1] of linear algebra. Although differential equations are used and discussed in this book, no previous course on differential equations is necessary. Thus v this Invitation is open to a wide range of students from engineering, science, economics, computer science, mathematics, and the like. This book is designed for the sophomorejunior level student who wants to continue exploring mathematics beyond linear algebra but who is perhaps not ready for highly abstract material. As such, this book can serve as a bridge between (for example) calculus and topology.
My focus is on ideas, and not on theoremproofremark style mathemat P ics. Rigorous proof is the jealously guarded crown jewel of mathematics. But nearly as important to mathematics is intuition and appreciation, and this is what I stress. For example, a technical definition of chaos is hard to motivate or to grasp until the student has encountered chaos in person. Not everyone wants to be a mathematician—are such people to be excluded ifrom the party? Dynamical systems has much to offer the nonmathematician, and it is my goal to make these ideas accessible to a wide range of students. In addition, I sought to 
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