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 159: Introductory page**

**Pages 160-161: It would be a bit too intense… // Story #1 is about a galloping horse.**

**Pages 162-163: One way to calculate average velocity… // Fortunately, we can find this limit…**

**Pages 164-165: But in addition to calculating average velocity… // We just covered two different ways…**

**Pages 166-167: Story #2 starts when we take two basic facts about circles… // We can use the tools from Chapter 7…**

MB: p. 166 Draw a circle and a tiny ring around it of width dr. Area of ring is 2 pi r dr.YB: I think this is fine as-is, and I don’t want to have to introduce infinitesimal widths like dr.

RC: Circles and rings – example?YB: Sorry, I’m not sure I understand this comment.

**Pages 168-169: The next part of story #2 is about rings. // But another way to calculate the area of a ring…**

MB: p. 169 The area of the ring is not the sum of the circumferences!!YB: We will try to finesse this.

**Pages 170-171: Of course, these two ways to calculate area… // This story about area isn’t a proof…**

MB: p. 171 Your analogy isn’t quite right: area= integral of circumference times thickness. Distance = integral of velocity times time.YB: All we’re saying is that they’re related, and that’s true. It doesn’t have to be a perfect analogy IMHO. Kind of like “greenhouse effect” :).

**Page 172: And there’s a bonus…**

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