Table of Contents
General comments here!
RB: On first impression, I like the mountain motif! It brings to mind the approach of https://www.youtube.com/watch?v=OmJ-4B-mS-Y (Map of Mathematics), and adds a topology.
RW: This is fun! I’m a little confused about the audience age. Sometimes it seems its for HS and sometimes for college. Generally i don’t have a lot of comments – I used to teach this stuff and I found it both entertaining and enlightening.
DLJ: There are two important things about limits, it’s important to keep them separate, and most textbooks don’t.
Important Thing Number One is that Bishop Berkeley objected to the whole calculus proposition, because infinitesimals can’t exist, and a whole lot of other hooey. The debate went on for decades, and “at the limit” was the verbal formula that eventually made all the Berkeley types shut up. This is a historical curiosity, or horror-story, all PhD’s know about it, and when they get around to writing calculus texts, they natter on about limits for ever and ever because they have this fixation that they’re historically important. Ugh.
Important Thing Number Two is that in this world we can never know anything with certainty. Certainty is the business of belief, and hence of religion. Science is the best we can do with the limited knowledge we have and our feeble powers of reason, so it’s naturally never certain. Therefore we’re always doing the best we can with whatever it is we’ve got.
(The brilliant Herb Simon, winner of one of the early Nobel Prizes in Economics [oops, you knew that...] coined the term “satisficing” in the hope that he could make the world do better policy by not forever and always striving for perfect policy. Great idea. Complete failure!)
It’s OK for the kids to know about all that Bishop Berkeley stuff in the abstract, but they should not have their time wasted on a whole lot of uphill-downhill reworking the debates of 300 years ago. What they need to know is, yes, there’s a big philosophical point there, but here, in this subject, we’re going with the best approximation we can get.
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