I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on what I teach my students on the first day of calculus in order to start the transition from Precalculus and to get them engaged for what we’ll be doing throughout the semester.

Part 1: The two themes of calculus: Approximating curved things by straight things and passing to limits.

Part 2: Using the distance-rate-time formula to estimate how fast an accelerating object lands when dropped from a tall building.

Part 3: Passing to limits to precisely calculate the above velocity.

Part 4: Using rectangles to estimate the area under a parabola.

Part 5: Passing to limits to precisely calculate the area under a parabola.

Part 6: Final comments: these two questions apparently have nothing to do with each other, but are in fact highly interrelated. The connection between these two topics, the Fundamental Theorem of Calculus, is one of greatest discoveries in the history of mankind, which my students are now privileged to understand at the ripe old age of 18 or 19 years old.

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