861.符号法* 4/48回 86符号法* 运算微积的原始形式是符号法 函数q()的n阶导数可以看成求导算符p=是在函数q(t)上作 用n次的结果,p"q(t)=nq(t).算符p的“倒数”1则解释为积分算 符,q()=0q(T)d.例如, ldτ=t,1 1dtdt==t2 依此类推 (6.1-1) 无限电工程师承 Heaviside把符号法应用于求解线性匪分方程 从而大大促进了符号法的应用.例如,电阻R和自感L串联电路匪 ●Fist●Prev·Next●Last● Go Back● Full Screen●cose●Quit• First • Prev • Next • Last • Go Back • Full Screen • Close • Quit §6.1. ÎÒ{∗ 4/48 §6.1 ÎÒ{∗ $Ž‡È©/ª´ÎÒ{© ¼ê ϕ(t)  n ꌱw¤¦ŽÎ p = d dt 3¼ê ϕ(t) þŠ ^ n g(J§p nϕ(t) = d n dt nϕ(t)©ŽÎ p “ê” 1 p K)ºÈ©Ž Χ1 p ϕ(t) = R t 0 ϕ(τ)dτ©~X§ 1 p 1 = Z t 0 1dτ = t, 1 p 2 1 = Z t 0 Z τ1 0 1dτdτ1 = 1 2 t 2 , daí§ 1 p n 1 = 1 n! t n . (6.1-1) Á>ó§« Heaviside rÎÒ{A^u¦)‚5ž©§§ l ŒŒr? ÎÒ{A^©~X§>{ R Úga L Gé>´ž