Invitation to Dynamical Systems PDF Download Ebook. Prof. Edward R. Scheinerman enables readers from a wide range of backgrounds and with limited technical prerequisites to explore the dynamical systems and mathematics in general. The book is designed for readers who want to continue exploring mathematics beyond linear algebra, but are not ready for highly abstract material.
Rather than a theorem-proof-corollary-remark style of exposition, it stresses geometry, intuition, and dynamical systems. An appendix explains how to write MATLAB, Mathematica, and C programs to compute dynamical systems. Scheinerman is a very energetic instructor in person, and he engages the class with a lot of interesting examples and demonstrations. So this book reads like a casual lecture, and it is informal. But his energy does not always translate well to text.
The structure of the book is similar to any intro textbooks whereas he lays a foundation and then builds. There are sanity checks as he adds more difficult concepts. And he uses the same basic example to contrast new material with what you have learned. And he does a great job of teaching Discrete and Continous systems at the same time.
There is also a more subtle idea illustrated here. In the picture there are a variety of fractal textures: the water, the clouds, the grass, and the trees. To compute the fractal dimension of a set, one overlays the set with grids of varying degrees of coarseness. The tiles surround the pool are therefore reminiscent of the box-counting definition of fractal dimension.
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