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.