作者dunerx0712 (orz)
看板trans_math
标题Re: [微分] 问一题微分方程式
时间Wed Jan 5 10:36:46 2005
※ 引述《artaniss (羽)》之铭言：
: R=(ln I-lnIo)/ln10
: Assume that Io=1
: (a)Find the intensity of the 1906 San Francisco Earthquake.(R=8.3)
: (b)Find the factor by which the intensity is increased if the Richter
: scale measurement is doubled.
: (c)Find dR/dI.
: 小弟不才,恳请各位前辈赐教
: 谢谢<(_ _)>
(a) Io = 1, R = 8.3代入,得
8.3 =( ln I - ln 1) / ln 10 ==> 8.3 * ln 10 = ln I
8.3 8.3
ln 10 = ln I ===> I = 10 =199,526,231.5 ........Ans##
(b) Io = 1
R = ln I- ln 1/ ln 10...........(1)
2R = ln I'- ln 1 / ln 10 ........(2)
2
===> (1)/(2) 得 1/2 = ln I / ln I'==> ln I'= 2 ln I ==> ln I' = ln I
====>两边取exp , 得 2
I' = I ............Ans##
(c) 两边对 I做微分,其余视为常数
dR/dI = ( 1/ I - 0 )/ ln 10 = 1/ ln 10 *I .........Ans##
题目不难,只是要把观念弄清楚补比较重要,加油吧..............^^....
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◆ From: 140.114.212.82
1F：推 artaniss:感谢喔^^可是第二题答案给１０的R次方耶? 163.25.118.38 01/06
2F：推 dunerx0712:是嘛,可是题目好像是说R要两倍,理论上答案 140.114.212.82 01/06
3F：→ dunerx0712:应该不会在出现R的变数,或是我算错....><" 140.114.212.82 01/06