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.

RC: Really like the hiking analogies throughout, naturally, and the types of examples for instance on pg 128 for marginal analysis. YB: Thanks!

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

RC: And….Will there be any other applications besides the ones under the headings of economics and physics in addition to the ones you have here – rabbits, patterns etc? For example Medicine – drug dosing, antibiotic resistance; food production; endangered species, etc – there are some really cool social science papers out there…I know some people say it’s so *obvious* you’d want to learn calculus, but I’m really partial to these non-typical examples (relationship calculus, chocolate-truffle calculus? etc) b/c typically it’s so easy to overlook calculus and modeling as an unnecessary evil that you don’t need unless you want to be an engineer or economist. Additionally, in college these are often weed-out classes for engineering or economics or even climate change studies…which leaves kids entering college wanting to be an engineer and leaving as a marketing major. Which is fine, except too often they hate calculus (and science); which imo is unfortunate for them (and feeds into treacherous politics). YB: This is a really good point, we will try to cover examples beyond engineering and economics. Population biology is a good one. I’m not sure what other non-typical examples you might have in mind, but I’m open to them :)

Page 14: And in addition to learning about calculus…

RC: The “big ideas”: Nice intro to the book, differentiating it from a textbook. Is there a “big idea” for each chapter? Is it more important than a “summary”? Will you call them out in a box? Or maybe that would be too much like a regular textbook? Maybe all this will be familiar to people who have read the rest of the cartoon series? YB: Not every chapter has a “big idea”, and in any case our style doesn’t involve call-out boxes :(

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

Join My Email List