Step one: get a bunch of other big fat Calculus books
Step two: spread them out in front of you
Step three: worry that your book will not be complete unless you include the union of all that they include
Step four: write a book that is like all the other books that have come before you
At the end of this process you have a book that is enough like Thomas or Stewart or some other well known book to make it easy for your publisher to market. There’s nothing wrong with that, but why then should someone buy your book and not one of the existing ones. If your book is just like Thomas then why not buy Thomas.
On the other hand, if it’s nothing like Thomas then there should be a good reason for that. Some books have differentiated themselves on supplements and adoption or non-adoption of technology. Others have been reform books. There are also those that target a subset of the market (Calc for Business students, Calc for Science majors, Calc for Engineers).
If you only targeted Math majors you wouldn’t sell very many books. So one solution is to create a book that aims to serve all of these audiences and let the instructors pick and choose which subset of the book to use.
Underwood Dudley has warned about books that get written for the Mathematicians teaching the course and not for the students taking it. I’ll say more about his essay later – but the result is a big fat Calculus book.
People fear that the opposite of those oversized books is a dumbed down calculus.
Two of my favorite books are relatively small and light and not dumbed down. One is Frank Morgan’s “Calculus Lite” and the other is Sylvanus Thompson’s “Calculus Made Easy” which has been reissued with help from Martin Gardner. I’m sure I’ll come back to these two later as well. In the mean time, Paul has just lent me three big fat calculus books. They are really heavy so they must be full of really good things.
The second book that I co-authored was a big fat book. Our editor was committed to providing quality and not just bulk. The series format, however, required bulk as well. The earlier books had been heavy but mostly they reprinted documentation that was freely available on line. Once we assumed that people could access this documentation, we were free to fill the pages with content that mattered.
Extreme Teaching 
February 22, 2006 at 10:11 pm
At this point, why call it calculus?
The word calculus even sounds daunting. Advanced or intermediate mathematics sounds just as intimidating.
Why not say predicting the future through mathematics.
The idea is teach a concept that is later used to solve some problems. What are the problems that likely readers will be solving or could solve?
Point: My calculus and DE are in the attic somewhere. But my Applied Finite Mathematics is on my shelf next to my other computer books. Why? Set Theory, probability, statistics, and some other cool stuff I might use from time to time.
February 23, 2006 at 12:40 am
I found this blog through Creating Passionate Users, and I can’t tell you how excited I am about your blog! As an engineering student, I always hated the ugly math I had to suffer through, and it wasn’t until advanced linear algebra when I rediscovered my love of math that started when I first learned calculus. I hope your book succeeds I creating many more passionate math students and removing the rote learning that most students resort to to get through their calc classes. Best of luck!
February 24, 2006 at 1:02 pm
Oh how I wish I had had a Head First Calculus book when I was in high school. This can be such a wonderful thing, especially for the self-taught type. I was in love with physics at an early age and as a 10th grader, I would spend a lot of frustrating hours over at the local community college trying to teach myself Calculus from these huge dry tomes. I remember finding Calculus Made Easy and devouring it after reading Richard Feynman’s stories about teaching himself Calculus as a young student. Every math book should be geared toward such self-discovery, even if its part of a course. I promise you there will be a boy or girl just like I was, entranced by physics or engineering or something and he or she will just not want to wait to unlock its secrets. They will wander through the local library or poke around at the local community college or on Amazon and when they stumble on your book, it will be like stumbling on a little pot of gold. They will be giddy, because someone will have realized that Calculus is worth being passionate about and kids haven’t yet been taught otherwise.
October 27, 2006 at 8:41 am
Leggo ed imparo sul vostro luogo. grazie!
April 25, 2007 at 1:11 pm
Thank You
January 1, 2010 at 3:10 am
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