无痛微积分

Painless calculus without more proofs

以“区间微积分”代替现行的“点态微积分”,从而使微分、积分和基本公式三者都隐含在一个微分的定义之中,无需另证。这样,三者可以一气呵成,只要一堂课,无需一学期。这样的微积分,不难、不长、无痛,使数学跟物理教学同步,不再拖物理教学的后腿。

This simplified calculas isnothing but picks up an old definition of differential （over every segment） and then adds up those differeistials to give an integral and its fundamental calculating formala with out a proof. Thus, using this old definetion,the three things, differential-integral-fundamental formula, can be done at a stretch, and taughtin one lesson without one semester,such a calculusis then nothing hard,long or painful, Mathematics and physics can then be taught in step.