Cartoon Calculus: Ch 1 (Introduction)

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 1: Part One (introductory page)

RS: On Ch 1 / Introduction, I like set up of the two mountains, but I think it should come a bit later. I think setting up the two characters of Netwon and Leibniz is more interesting and more appealing. I also want to know a little bit more about their philosophies and perspectives, and I think this could be compelling for the reader. YB: Probably too late for us to adjust this.

Page 3: Calculus is about two mountains.

Pages 4-5: Derivatives are about measuring rates of change. // Integrals are about measuring lengths, areas, and volumes.

MB: I am surprised to see on Page 1 that you say integration is used for lengths, areas and volumes… a very limited (and maybe misleading) statement? YB: Hm… what would you say it’s for? MB: Well, for adding anything. You can integrate the total temperature change in the 20th century, or any other time dependent change; you can (as you say later in that famous apple eating astronaut problem) find the total energy needed to do something… YB: Good point. Maybe edit to something like “adding things up, like lengths, areas, and volumes.”

Page 6-7: It may not seem like these mountains have much in common… // In this book we’re going to start with an overview…

Pages 8-9: The big ideas of calculus go back hundreds of years… // Unfortunately, these big ideas have been obscured by two more recent developments.

BG: suggest using pi because people recognize it as both math and greek. I don’t think that’s the case with epsilon or delta. YB: I think we can do them all!

Pages 10-11: The first avalanche was mathematical rigor. // Making the journey safe took away some of the excitement…

RS: I don’t like the idea of rigor and formulas being “avalanches.” I think these are really two sides of the same coin. But I do think the notion of safety equipment or perhaps maps and measurement are really good ways to reference the concept of “formality.” YB: Rigor and formulas are I think different issues; one is about intellectual foundations and the other is ultimately about stuff to memorize. And Yes about safety equipment!

Pages 12-13: Calculus turns out to be so useful… // This book is different.

BG: choice – I’d choose “building bridges” because most people can relate to a bridge. “engineering” and “quantum mechanics” are more abstract.

Page 14: And in addition to learning about calculus…

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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