欧拉等式讲: 对 求导及积分: 即 的微积分运算变为其本身的代数运算。有什么用? 电子线路里的基本电子元件为电阻 ,电容 , 电感 , 其中: 如果信号 是单一形式的三角函数 , 而我们又可以把它写为 的形式的话 (比如, ), 则 , , 组成的线路的表达方程可由微积分形式变为线性的代数形式,从而简化运算。 phasor, 即 ,就是为了达到这个目的: 微分即相位移正90度,积分即相位移负90度,加上相应的 修正。 除了简化微积分,phasor亦可形象地表示循环振动,波动,如图。 注意圆圈里运动矢量在横轴上的倒影正是 。 A phasor is a complex number that represents the amplitude and phase of a sinusoid. 参考资料: 【1】John Semmlow, 'Circuits', Signals, and Systems for Bioengineers, 2005 动画来自 wikipedia .
作者:蒋迅 我发现了一篇我在1988年为完成英语课作业写的短文,谈的是我做微积分课助教的体会。记录在这里。那时候我的英语水平很有限,在这里献丑了。 Nothing has been more rewarding than working as a Calculus lab instructor. In the lab, because of its small size and informal nature, students can discuss, freely, their particular difficulties. As the group leader, I turn these individual questions into general discussion topics. And by repeating this process in many different forms, I eventually begin to see my objective achieved: frustration and confusion transformed into enthusiasm and understanding. It is this transformation from confusion to the understanding capable of most Calculus students that makes my job worthwhile.