浅谈高等数学在高中数学教材中的渗透——以人教A版为例

A Brief Talk on the Infiltration of Advanced Mathematics in Senior High School Mathematics Textbooks—Taking the People’s Education Version A as an Example

摘要: 学生学习知识是一个连贯的过程，做好小学与初中、初中与高中、高中与大学的衔接至关重要。高中数学知识与大学数学知识联系密切，教材习题的编制、高考试题的命制常会以高等数学作为背景。本文例析函数的凹凸性、重要极限、泰勒公式、直线的点向式方程与平面的点法式方程在高中数学教材中的渗透，并由此得到一些教学启示。

Abstract: Students’ learning knowledge is a coherent process. It is very important to do a good job in the connection between primary school and junior high school, junior high school and senior high school, senior high school and university. The knowledge of high school mathematics is closely related to the knowledge of college mathematics. The compilation of textbook exercises and the formulation of college entrance examination questions often take higher mathematics as the background. This paper analyzes the penetration of concavity and convexity of function, important limit , Taylor formula, pointwise equation of straight line and point normal equation of plane in senior high school mathematics textbooks, and obtains some teaching enlightenment.