Dynamical Systems Self-Directed Project

Book: Kenneth R. Davidson Allan P. Donsig

Real Analysis and Applications

In Chapter 11 of the textbook, Discrete Dynamical Systems, read:

to Chapter 11

Fixed Points and the Contraction Principle

Newtons Method

Orbits of a Dynamical System

Periodic Points

Chaotic Systems

Iterated Function Systems

Note that you may need to read parts of Chapter 9 to support these readings.

In Chapter 12, Differential Equations, read:

to Chapter 12

Integral Equations and Contractions

Calculus of Vector-Valued Functions

Differential Equations and Fixed Points

Solutions of Differential Equations

Local Solutions

Linear Differential Equations

Perturbation and Stability of DEs

Note that you may need to read parts of Chapter 9 to support these readings.

written summaries and worked exercises

From the readings above, select two readings from Chapter 11 and two readings from Chapter 12 that were the most interesting to you. For each of these selected readings, submit a written summary and a worked exercise in a typed document with properly formatted mathematical expressions.

Instructions for the written summary

In your own words, provide an overview of the selected reading that introduces and provides relevant background on the topic and highlights the key results that are presented in the textbook. Here, you should not simply restate the results, but explain their importance and draw links to previous results, both in the selected reading and when applicable to the core material presented in Units 17. You do not need to replicate all of the formal proofs and solutions that are presented in the textbook. Rather, select one important result and, in your own words, provide a reworking of the proof presented in the textbook.