Showing posts with label fractals. Show all posts
Showing posts with label fractals. Show all posts

The Art of Modeling Dynamic Systems: Forecasting for Chaos, Randomness, and Determinism (Scientific and Technical Computation Series) Review

The Art of Modeling Dynamic Systems: Forecasting for Chaos, Randomness, and Determinism (Scientific and Technical Computation Series)
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I find myself agreeing with all the comments made so far.
It's not too common to find a book that is able to describe in simple terms, such a large and diverse range of mathematical tools.
The author uses a framework - to tie together tools used in describing and handling deterministic, semi deterministic, and stochastic systems. For an example of Deterministic, try ODE's (ordinary differential equations), for semi deterministic - try Periodic but noisy wave-forms (some stock prices), and finally Stochastic - Random looking waveforms that have underlying patterns that can be described using either using Chaotic indicators (Hurst, Liapunov ) or probability type descriptors.
This book is the kind of thing you needed to help steer you through those dry mathematical books that are divorced from reality - A sort of classification system for deciphering what kind of gunpowder was used in those display's of intellectual fireworks from the tops of ivory towers. Kinda "So thats what all that maths means, but in plain english".
A depth of understanding, for practical application, without intellectual egotism and opaqueness. (But then maybe I'm just a bit thick ... :)
I'd tend to call this book as an equivalent to the Rosetta Stone for the maths of dynamical systems.
You may not use it directly - but you will benefit and grow in understanding from its' plain and simple sign posts along your journey.
It has its place on my book shelf.

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Introduction to Mathematical Modeling Using Discrete Dynamical Systems Review

Introduction to Mathematical Modeling Using Discrete Dynamical Systems
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This book introduces Mathematical Modeling without requiring a background in differential equations. I think it does so effectively, although I agree with the previous reviewer that some of the examples are trivial. If used as part of a college course, the instructor really ought to assign computational projects.
Some of the models presented in the book are very similar, but that is not an issue with the book. It seems like an effective way to get students to figure out on their own how similar models are connected. In later chapters, function families are introduced that show how the behavior of interest can be analyzed more generally. Working with pencil and eraser, I prefer easy models. In practical applications, it's all going to be done by a computer anyway.
There are other Mathematical Modeling books that will be more challenging. However, introducing these concepts in ways that require differential equations and linear algebra may just make it more difficult to focus on the new concepts. If you understand the ideas in these simple models, you will also recognize them in more advanced models.

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MATHEMATICAL MODELING USING DISCRETE DYNAMICAL SYSTEMS! This mathematics text introduces powerful mathematical modeling techniques while providing you with the tools you need to succeed. Exercises with answers, suggested computer projects with specific instructions for their completion, and the book-specific website are just a few of the tools that will help you master the material. Coverage of current research, such as dynamical systems, shows you that mathematics is a vibrant and evolving discipline.

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