This book grew out of my lecture notes for MAT 211 Calculus III at California State University, Dominguez Hills. It is an attempt to turn those notes into a concise text using PreTeXt, with particular attention to features that support the course well. One advantage of PreTeXt is that it allows interactive graphics, including live three-dimensional visualizations through Sage, and I have tried to make use of that where it helps students develop geometric intuition.
The treatment here is intentionally selective. This is not a detailed or fully rigorous account of calculus for functions of several real variables. In a number of places, I assume enough smoothness so that the objects under discussion exist and the main ideas can be developed efficiently. Likewise, differential forms are used primarily as a computational tool, without attempting a fully rigorous treatment in the body of the text.
My own understanding of this material has been shaped especially by [1] and [2], both of which are listed in the references. Their influence appears throughout this book, even when the presentation here is shorter and more course-focused.
