Chaos Under Control Sample Syllabus 2

David Peak and Michael Frame

1. Background (3 sessions, read Ch 1)

* same as Syllabus 1

2. Iterated Function Systems (6 sessions, read Ch 2)

* same as Syllabus 1 + a more careful description of coordinate transformations (possibly introduce matrices)

3. Fractal dimensions (6 sessions, read Ch 3)

* same as Syllabus 1 + the logarithm function

4. Dynamics: linear and nonlinear (7 sessions, read Ch 4)

* same as Syllabus 1 + extension to the limit of continuous change and the exponential function (possibly introduce the derivative)

5. Dynamics: period doubling (5 sessions, read Ch 5)

* same as Syllabus 1 + the derivative as the slope of the tangent line

6. Noise and detecting chaos (3 sessions, read Ch 6)

* same as Syllabus 1 + harmonic functions (possibly introduce the idea of Fourier analysis)

7. Controlling chaos (3 sessions, read Ch 6)

* same as Syllabus 1

8. Mandelbrot-Set (4 sessions, read Ch 7)

* same as 9 of Syllabus 1 + complex arithmetic

9. Fractal basin boundaries (3 sessions, read Ch 8)

* same as 10 of Syllabus 1 + Newton's method for root finding

10. Project reports by students & wrap-up (2 sessions, read Ch 10)

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