Cartoon Calculus: Back matter


Quick links to Front matter, Back matter, and:
Part One: Ch 1: Introduction, Ch 2: Speed, Ch 3: Area, Ch 4: Fundamental theorem, Ch 5: Limits
Part Two: Ch 6: Derivatives, Ch 7: Toolkit, Ch 8: Extreme, Ch 9: Optimization, Ch 10: Economics
Part Three: Ch 11: Hard way, Ch 12: Easy way, Ch 13: Revisited, Ch 14: Physics, Ch 15: Conclusion

MT: We appreciate that “tangent lines” is defined in the glossary, but think “instantaneous speed” and “differential calculus” should also be defined. YB: We will do this!

MT: On page 40, “integral calculus” needs to be defined in the glossary, especially because this chapter dumps a lot of new terms on students, and therefore as much clarity as possible is a must. YB: Yes, we will do this.

PH: Fundamental Theorem of Calculus: The First Fundamental Theorem F(b) – F(a) instead of f(b) – f(a). YB: Good catch, we will fix!

PH: Pythagorean Theorem: Pythagorean instead of Pythogorean YB: Good catch, we will fix!

DM: The Pythagorean Theorem glossary entry: if you are willing to include a small drawing in your glossary, the Pythagorean proof is very simple and intuitive. See “Pythagoras’ Proof” here. As a side note, I went to one of Edward Tufte’s presentations yesterday where he mentioned never having seen a good Pythagorean Theorem visual proof. I sketched that one down on the back of my business card, not knowing that it was the one due to Pythagoras, and gave it to him after the lecture. When I read your book today, I thought of the same proof and thought “maybe they link to it on Wikipedia” and discovered that it is in fact Pythagoras’ own proof. I found it, not attributed to Pythagoras, probably while a senior in college, and was blown away that it was so simple and intuitive and that nobody in any math class had ever put it on the board.

YB: For slope, add “rise over run”. For tangent line, cover kissing and surfing.

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