Let’s work through some of the math behind what it means to be a Complete Orthogonal System. To do this we are going to define what is means to be Orthogonal and what it means to Complete. We are going to jump around from idea-to-idea hopefully creating a full 360 degree picture.

This is going to be a little mathy. So I am going to try to avoid doing anything mathematically fancy. But there will be some math.

• Mutually Exclusive Collectively Exhaustive (MECE) – I always like to start with an English language example. It this case there is a prefect overlap with MECE, a tool writers and consultants use frequently. TASK #1 Write a two paragraph summary what you learned on this page!
• Simple Complete Orthogonal System – Here is an example of a simple Complete Orthogonal set with unit vectors. TASK #2 Write a one paragraph summary what you learned on this page!
• Getting Started with Fourier Math – Understanding how we can think about Fourier with Completeness and Orthogonally. Task #3-5 enclosed
• Fourier Example (TBA) – Ramp wave extra credit if worked out, please tell me before hand
• Legendre Math (TBA) – Extra credit if worked out, please tell me before hand
• Night of Fourier Madness – Do we want to do this?