MTH306 Non-Linear Dynamics Chaos

[3–0, 3 cr.]

This course covers the topics of iteration, fixed and periodic points, graphical analysis of iteration, stable and unstable orbits, attracting and repelling periodic points, iterations of a quadratic family, Julia sets, Mandelbrot sets, fractals, and chaos.

Course Learning Outcomes:

1. Students will be able to iterate functions, identify the orbits of seed values and analyze graphically such orbits.
2. Students will be able to find fixed points and identify them as repelling, attracting, or neutral. Students will also understand bifurcations.
3. Students will have a complete understanding of the real and complex quadratic families.
4. Students will be able to construct the Cantor Set and measure its length, construct the Sierpinski Triangle and measure its area, construct the Koch Curve and measure its perimeter.
5. Students will learn about the Julia and Manderbolt Sets.