简介了牛顿和莱布尼兹对微积分建立的贡献，探讨了极限和导数的动机. 通过剖析“绳子匀速拉船，求船速度和加速度”的案例，综合地将坐标系、矢量、微分加以应用. 使学生理解质点速度沿其轨迹切线方向的运动规律，及矢量投影分解的物理要求.

Starting from introducing the contributions of Newton and Leibniz for established calculus，we discuss the motivation of limitation and derivative. Through analyzing an example of“calculating both velocity and acceleration of a boat moved by equal speed”，the coordinate system，vector and differentiation are applied comprehensively. This makes students understand deeply the motion law of a particle and physical requirement of vector projection.