Calculus Teaching and Research Section

In August 18, the opening of the calculus Reading Room (trial run) will arouse the interest of many readers and may arouse the curiosity of some mathematics instructors. To this end, in June 2011, J. Keisler specially wrote the "Basic of Infinitely small calculus" (electronic version) for the mathematics instructors to answer questions and serve as the teaching guide book (material) of "basic calculus ).

According to the basic of Infinitely small calculus (15 chapters in total, 213 pages), we plan to open up the section of calculus for the majority of mathematics instructors to conduct teaching and research. This tutoring material tries to avoid the use of mathematical logic concepts. It only uses certain set theory terms. For the theorem of many traditional calculus, a rigorous proof of using an infinitely small method (or tool) is provided, which can open your eyes and promote the reform of Calculus Teaching.

In the calculus section, "frequently, standard results are given Alternate
Proofs using infinitesimals ", and," in some cases a standard result which is beyond the scope of beginning calculus is rephrased (Change statement)
A simpler infinitesimal result and used into tively in elementary calculus ", meaning that in some cases, for some difficult questions that go beyond the original horizons of traditional calculus, rephrased is a simple, infinitely small study. Wonderful! Wonderful!

For this purpose, in August 14, we uploaded the preface to the basic of Infinitely small calculus for your reference. In the future, we will follow the calculus reading room to continue uploading relevant materials and cooperate with the in-depth reform of domestic Calculus Teaching.