This paper discusses how to teach students"the product of infinite infinitesimals isn t necessarily infinitesimal" in teaching "advanced mathematics" Or "Mathematical Analysis",and the author provides some new original examples which had not been seen in currently available textbook and riches the teaching content.

A Note on The Theorem of Equivalent infinitesimal Replacement;

On the product of infinite infinitesimals;

On equivalent transformations of infinitesimals and their popularization;

Theorem 1 and 2 about ratio of two infinitely small quantity function monotonous are obtained.

In this paper,we disscus the poerations of infinitely small quantity and get some result.

In this note, we construct some examples to show that the infinitely product of the infinitely small quantity may be not infinitely small quantity.

The Extension and Application of the Equivalent Infinitesimal Replacement;

An infinitesimal equivalence theorem is established in this paper.

This paper takes the infinitesimal as an entrance to derivative and shows the essential of derivative concept step by step and therefore enhances the students to comprehend this concept.

In this paper,the link between infinitesimal quantity and some important notions in differential and integral calculus,and the simple application of infinitesimal in limit operation are discussed.

In teaching mathematics, we should use geometric figures more in explaining concepts, attach importance to ratio limit and infinitesimal quantity, employ the regular methods, pay attention to the specific skills and help them analyze and solve problems.