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Outline of the video
Motivation: why we need the notation, intuitive understanding using graphs
Definition of the big-O notation
Example: sin(x)=O(x) as x approaches 0
Cute cat break
Theorem: Necessary condition that f(x)=O(g(x)), how to verify the last equality using a limit of f/g
Proof of the Theorem
Examples: x^2+x+1=O(x^2) as x approaches \infty, x^2+x+1=O(x^3) as x approaches \infty, and x^2=O(x^2+x+1) as x approaches \infty
Example: O(x^2)+O(x^3)=O(x^2) as x approaches 0
More examples: Properties of the big-O notation