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Mathematical Modeling

Dynamical Systems

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Polytechnic School's

Mathematical Modeling II with Calculus BC


About This Site

This site was specifically designed for the students in Polytechnic School's Mathematical Modeling II with Calculus BC course (MMII/BC), but, of course, anyone is welcome to drop in for a visit. For the MMII/BC students, the site should be used as a supplement to what you are learning in class and as a starting point from which to explore extensions of the classroom topics. The web site alone cannot begin to give you detailed instruction in the mathematics of dynamical systems, chaos theory, fractal geometry, and the "C" topics from the BC Calculus syllabus.

The navigation buttons on the left side of each page will take you to other pages within this site, while the buttons on right side take you outside the MMII/BC site. Clicking on any of the buttons on the right will open a new page in your browser. Here are brief descriptions of what awaits you when you click each of these outside link buttons.

Polytechnic School--This link takes you to the home page of Polytechnic School, the institution without which none of this would be possible.

The Non-linear Lab--This site gives a rather detailed introduction to the ideas and the mathematics behind chaos theory. It focuses more on continuous systems than on discrete ones and so provides a nice complement to our emphasis on discrete dynamical systems in the MMII/BC class.

UT Austin Chaos Site-- Here is an easy to follow introduction to the history of science pertaining to the discovery of chaos theory, including a discussion of the philosophy of determinism.

Boston University's Dynamical Systems and Technology (DYSYS) Site-- This is Professor Robert Devaney's wonderful site where you can learn more about the Mandelbrot Set (one of the icons of Chaos Theory) than just about anywhere else on the web. There is much more on this site as well, including an analysis of Tom Stoppard's amazing 1993 play Arcadia, which is full of references to chaos theory and fractal geometry.

Chaos and Fractals FAQ--Here you will find answers to frequently asked questions about chaos and fractals. A lot of them!

Visual Calculus--Here are some nice lessons and tutorials on various topics from calculus developed at the University of Tennessee at Knoxville.

College Board AP Calculus--This is the "official" AP Calculus site from the people in charge of the entire Advanced Placement Program.

Java Applets for Calculus--If you are a visual learner or are just a big fan of animations, this is a place you should enjoy.

Email Mr. Robinson--In case of emergency, here is a direct line to the teacher of MMII/BC.

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Links

Polytechnic School

The Non-linear Lab

UT Austin Chaos Site

Boston U. DYSYS Site

Chaos & Fractals FAQ

Visual Calculus

College Board AP Calculus

Java Applets for Calculus

Email Mr. Robinson