Hello everybody,

Welcome to Fall 2019's version of MAT332 - Introduction to Nonlinear Dynamics and Chaos! Please take your time to go through the syllabus and published modules to familiarize yourself with the course. We, the instructor (Kasun) and the TA (Hossein), are here to help you succeed in this course. Please attend the lectures and tutorials regularly, and participate in the discussions by asking and answering questions. Lectures start on September 5th and tutorials start on September 9th.

Our goal in the course is to understand systems that seem to be behave randomly but are completely deterministic. These systems are called chaotic dynamical systems. They have baffled mathematicians and scientists for centuries. But during the last 50 years or so, there's been an explosion of related research work that has improved our understanding. We'll learn several mathematical theories about these systems and apply them to some examples. We'll also learn about some applications of this area of mathematics to science and engineering.

But before we start, let's look at these cool pictures and admire their beauty. Hopefully, by the end of the semester, you'd be able to understand the mathematics behind each one of them. Good luck!

"Chaos theory is often described from a negative viewpoint: the high sensitivity to initial conditions makes it impossible to practically determine the future evolution of a system, because these initial conditions are never known with total precision. Yet, the theory would be rather poor if it was limited to this absence of determinism and did not encompass any deductive aspect. On the contrary, I want to insist on the fact that, by asking the good questions, the theory is able to provide rich and nontrivial information, and leads to a real understanding of the dynamics." - quoted

The Lorenz Attractor (This image was taken from this link and the copyrights belong to the original creator).

The Koch Snoflake (This image was taken from this link and the copyrights belong to the original creator).

mendelbrot set.gif
The Mendelbrot Set (This image was taken from this link and the copyrights belong to the original creator).