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Differential Equations, Dynamical Systems and Introduction to Chaos

 

I read this book quicker than I wanted to. It will be a wonderful resource to come back with the explorations and the exercises.  As such this review pertains to reading rather than getting the most out of this book.  This limitation aside, this is a very clearly written and illustrated book.

There is a progressive increase in complexity proceeding from one dimensional linear autonomous differential equations, to linearisation of non-linear equation, qualitative assessments through analysis of equilibrium points, Poincare maps. The section introducing chaos (focussing on hallmarks of density of periodic orbits, transitivity and sensitivity to initial conditions) is very interesting. I found the chaotic behaviour of logistic map and relation (homeomorphism) to Cantor sets very interesting.

It is a very good textbook and I look forward to a time when I can maximize my learning by diving into the explorations (esp. with Mathematica).

 

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Categories: books, Mathematics
  1. October 29, 2012 at 6:45 pm
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