Originally Posted by HowlerKarma
Seriously, guys-- we HAVE thought about this. A lot, even. We're also very familiar with the system, having been college faculty (in STEM).

It's why I tried to explain initially WHY I needed advice on particular materials and what type of learner my DD is, rather than asking if it is a good plan to start with. I realize that the unsolicited advice is well-intended, but we really wouldn't be doing things the way that we are if we had good alternatives.

OK. After the Brown book I suggest a relatively short book

http://www.amazon.com/Analysis-Elementary-Functions-Robert-Sorgenfrey/dp/0395340578
Analysis of Elementary Functions
Robert H. Sorgenfrey and Edwin F. Beckenbach

that provides a bridge from trigonometry to calculus, and/or "Modern Introductory Analysis" by Dolciani et al (there are several editions).