Cartoon Calculus: Ch 15 (Conclusion)

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 187: That was exhausting…

Pages 188-189: It’s tempting to think that calculus is the pinnacle… // That’s because mathematics is about finding patterns…

Pages 190-191: The calculations of pi in Chapter 3… // If you think those examples are trippy…

MB: p. 190 ? Are the right hand pictures supposed to be the limiting figures??????? How can this be? They are just figures along the way to the limits, aren’t they? YB: I’m tempted to just reply that you need to look at them more closely!! :) Seriously, we will ponder, but I think this is probably fine as-is.

Pages 192-193: For another example of limits, consider prime numbers. // It turns out that these precise answers…

MB: p. 193 If you are going to use the symbol ln, then define it. YB: No space, and I think this is fine.

MB: On graph, label axes (maybe use ’n’, not ‘x’).

MB: Symbol x-> infinity should be down below.

MB: I think this example is too abstruse. YB: Agreed that it’s challenging, but it’s a really neat application so I think it’s worth it.

Pages 194-195: And of course we use limits in calculus… // …and integrals…

Pages 196-197: Calculus applies to rabbits because… // The mathematical result is called a differential equation…

MB: p. 197 This will be unintelligible to most of your readers, I would think, but if you want to use it, explain what equation is doing and define P_o YB: I agree that this is tricky, but I’m not sure if more verbiage will help.

Pages 198-199: Another advanced topic… // Multi-variable calculus…

MB: p. 199 Ditto. Show a picture, define all terms (P_L, P_K) or don’t do this.

Page 200: In short, there’s plenty more to study…

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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