It finds slopes on curves,
And areas inside curvy shapes.
So it can find a changing velocity,
Like with gravity.
How does it work?
We use two points to find slope of a line, rise over run.
But we want the slope of a curve at one point.
So Newton and Leibniz “cheated”,
Putting the two points infinitely close together.
It works.
If you want to learn more,
Althea and her friends are exploring calculus
And you can join them.
(Email me at altheasmathmysteries@gmail.com.)
The front image is much nicer now. It's still not a professional illustration. That will happen after we begin our kickstarter campaign, and that won't be for many months, at the earliest.
I decided the predictability of having Althea's Math Journal after every chapter would feel good to readers. But the first two Mondays had two chapters each, and she can't be writing her journal in the middle of a gathering. So I had to combine chapters 1 & 2 and also chapters 5 & 6. Done.
Also, at 450 pages, the book is way too long. I intend to shave off at least 100 pages. I found some bits in chapter 1 that could go. (Some of that appears in the Activity Book still.) So that chapter is a reasonable length, I think. So far, I haven't found anything to take out in what is now chapter 4. I hope folks giving me feedback can help me with that. I think it comes in too long at 26 pages.
I'm still finding places where I need to add a bit to make the math clearer. But more and more, I'm also finding bits that can go. Adding a touch of color here, removing something out of place there. I feel like a sculptor or painter. Ahh.
I wish it were easier to find beta readers. (I have a story to tell about that. It will be in a blog post soon.) If you're interested, email me at altheasmathmysteries@gmail.com.
Table of Contents
Here it is. Does it entice you?
Prologue
Part 1. Slopes on Curves and Changing Velocities
Ch. 1. Areas and Graphs
Ch. 2. On Our Own
Ch. 3. Working On Our Icons
Ch. 4. Velocity, Acceleration, and Tangents
Ch.5. Finally, the Derivative
Ch.6. Measuring Speed
Ch.7. Derivatives from Graphs
Ch.8. Even More Perspectives
Ch.9. Finishing Up and a Test
Part 2. So Many Derivatives
Ch.10. All the Powers
Ch.11. Polynomials and Graphing
Ch.12. Graphing with Newton
Ch.13. Back to Trigonometry
Ch.14. Derivatives for Sine and Cosine
Ch.15. Quotients and More Trig Derivatives
Ch.16. Optimizing
Ch.17. Nested Functions
Ch.18. Exponential Functions
Ch.19. Exponential Derivatives
Ch.20. Implicit Derivatives
Ch.21. Linearization
Ch.22. Review and Another Test
Part 3. Anti-derivatives, Areas, and Volumes
Ch23 Areas
Ch24 Getting Closer to Area
Ch25 That Area Definition
Ch26 Fundamental Project
Ch27 Gravity
Ch28 Substitution
Ch29 Volumes of Revolution
Ch30 A Final Exam
Ch31 Back to Infinity
Ch32 Infinite Series
Ch33 Infinite Series for Area
Epilogue.
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