开宗明义，第一章的第一句话是：“Chapter 1 takes the student on a direct route（直达路线） to the point where it is possible to study derivatives（研究导数）.”
00后大学生听了这话，无不好奇：十个课时就会计算导数？呵呵！
这里的奥秘就是引入超实数。如此安排，世界上的微积分教课书“独此一家”，别无他人。
敢于“吃螃蟹”的数学教员，无比荣耀。我们祝贺你取得成功！
袁萌 陈启清 8月28日
附：微积分手机版第一章内容说明
REAL AND HYPER REAL NUMBERS
Chapter 1 takes the student on a direct route to the point where it is possible to study derivatives. Sections 1.1 through 1.3 are reviews of precalculus material and can be skipped in many calculus courses. Section 1.4 gives an intuitive explanation of the hyperreal numbers and how they can be used to find slopes of curves. This section has no problem set and is intended as the basis for an introductory lecture. The main content of Chapter 1 is in the last two sections, 1.5 and 1.6. In these sections, the student will learn how to work with the hyperreal numbers and in particular how to compute standard parts. Standard parts are used at the beginning of the next chapter to find derivatives of functions. Sections 1.5 and 1.6 take the place of the beginning chapter on limits found in traditional calculus texts. For the benefit of the interested student, we have included an Epilogue at the end of the book that presents the theory underlying this chapter.
1 THE REAL LINE （……以下省略）