“数学结构”在一元微积分教学中的应用浅析

Analysis on the Application of Mathematical Structure in the Teaching of Unary Calculus

一元微积分作为高等数学的基础,拥有大量的数学运算,同时蕴含着一系列经典的运算理念和数学思想.无论极限、导数、微分、积分,均不同程度地体现了数学的“结构性”,特别是在微积分基础阶段的教学中,持续渗透“数学结构”存在价值.培养学生的“结构”构建意识,反复体会“数学结构”的重要性,对多元微积分及级数的学习,甚至于微积分在更广泛领域内复杂计算中的应用都有十分重要的意义.

As the foundation of advanced mathematics,unary calculus has a large number of mathematical operations,and contains a series of classic arithmetic concepts and mathematical ideas.Regardless of the limit,derivative,differential,and integral,they all reflect the"structure"of mathematics from varying degrees.Especially in the teaching of the basic stage of calculus,continue to penetrate the value of"mathematical structure",cultivate students'awareness of"structure"construction,repeatedly realize the importance of"mathematical structure",learn multiple calculus and progression,and even the application of calculus to complex calculations in a wider field are of great significance.