Video of lecture.
Handwritten notes from lecture.
Waiting room video: interview with Curtis McMullen.

We considered a stone being dropped from the top of the Leaning Tower of Pisa. We assumed that the distance at time t is 4.9t² (something physicists tell us should be true). We used the formula y= 4.9t² to begin a discussion of functions. We then investigated the question: what is the speed of the stone at time t=2 seconds?

The lecture touched on the notions of "continuous function", "limit" and "derivative" (="speed"). The remaining 23 lectures in Semester I will provide more details on these three fundamental notions.

The lecture also included reference to a function which was shown by Karl Weierstrass to be everywhere continuous (no breaks in its graph) and nowhere differentiable (no point on its graph has a well-defined tangent). The function was a lesson to physicists for the need for rigour.

For a more detailed summary of what calculus is all about, read the section "A Preview of Calculus" in Stewart, pages 2-9,

For more details on the Weiertrass function see here.