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泰勒公式是古典微积分的顶峰,它在理论上深刻揭示了函数性态,在计算上能有效地确定函数的精确值和近似值,这就使得它在微积分教学中成为一个重点和难点。为在教学中突出这个重点、解剖和分散这个难点,就要有计划,有步骤,有针对性提出一些问题,启发学员产生共鸣,然后逐一地加以解决。下面是我们在教学中提出的三个问题: 一、为什么要讲泰勒公式? 在此以前所学的许多函数(主要是初等函数),除了多项式以外,它们的定义有些
Taylor’s formula is the peak of classical calculus. It profoundly reveals the function state in theory and can effectively determine the exact value and approximation of the function in calculation. This makes it a key and difficult point in the teaching of calculus. In order to highlight this important point in teaching, dissect and disperse this difficult point, we must have plans, steps, targeted issues, inspire students to resonate, and then solve them one by one. Here are the three questions we raised in our teaching: First, why should we talk about Taylor’s formula? Many of the functions learned so far (mainly elementary functions) have some definitions other than polynomials.