Progress: Althea and the Mysteries of Calculus, version 8.2

 

Minor changes

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.