Calculus for Everyone I wrote a free Calculus I textbook (Differential Calculus) as part of Brooklyn College's contribution to CUNY's Open Education Resources (OER) at CUNY. The College supported this effort by giving faculty participating in OER a 3credit course release for Spring 2015. At some point in the future I will also write a free Calculus II textbook (Integral Calculus).
The most updated version was posted on Feb 9, 2018. Calculus for Everyone (Chapters 1  11) It may help to read the preface before reading the chapters since that is where I describe my views on how to make Calculus textbooks accessible to a wide audience and discuss the various types of Calculus courses. The following excerpt from Skimming a Century of Calculus guided my approach.
On page 48, R. G. Helsel and T. Radó pondered (MAA 55 1948, pp. 2829) the question Can We Teach Good Mathematics To Undergraduates? They cited three ingredients of good mathematics: relevancy (calculus, for example, is overflowing with relevancy), rigor (all of the reasons must be given), and elegancy (not to deprive the students of the very thing that affords us our greatest pleasure). Consistency, I thought, they did not mention consistency. Clearly the question at hand is that of good mathematics presentation. For a good course, consistency in style is a prerequisite. It could be a trifle. For example, if during the first few weeks Professor conditions the students by emphasizing important ideas with a chalk of red color, and then comes to a lesson without his implements, many students will be bound to miss something important.
Consistency is something that I found missing in textbooks and it is not just the layout of the material, but a consistency of thinking style, consistency of ideas and of how to start with something simple and build up from there. I paid attention to consistency as best as I could. If you read the book (or portions of it) or use it in your class, I would love to hear from you. Constructive criticism would be much appreciated. You can send me email at Sandra Kingan (skingan@brooklyn.cuny.edu).
