Cartoon Calculus: Ch 4 (The fundamental theorem)

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

Page 43: Whee!

Pages 44-45: So far we’ve learned that derivatives… // Integrals involve adding up things…

WM: Page 44 – you state that we’ve learned what “derivatives” are, but unless I missed it, you haven’t used that word in the book yet. You’ve said that we solve these problems using “differential calculus”, but a beginner won’t know the relationship between the two words. (I expect this is a side effect of writing the chapters out of order.)

Pages 46-47: Now, we all know that… // It turns out that…

WM: Pages 46-47 are very clever.

Pages 48-49: To continue the analogy… // It turns out…

Pages 50-51: The math of the fundamental theorem… // There’s even an easy way…

MB: on p. 50 you say derivatives and integrals are ‘opposites’. They are, rather, inverses of each other: any person who has had a class in high school math will have heard of inverse functions, and the idea that one operation inverts another is attractive. YB: Good point, but it’s a question of whether the greater precision in language is worth the confusion it might cause for folks who don’t know what inverses are.

WM: Page 51 – “squiggly line on a graph” might be confusing. The Squiggly line IS the function, but a reader might think you mean the axes are the function. (I’m not sure I’m being clear here about where I think the confusion lies, but my solution is to say “squiggly line on a coordinate axis”.)

Pages 52-53: We can use the integral… // It’s pretty obvious that…

WM: I don’t quite follow your argument on page 53.

Page 54: It’s a little harder…

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

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