作者dunerx0712 (orz)
看板trans_math
標題Re: [微分] 問一題微分方程式
時間Wed Jan 5 10:36:46 2005
※ 引述《artaniss (羽)》之銘言：
: 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,懇請各位前輩賜教
: 謝謝<(_ _)>
(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
====>兩邊取exp , 得 2
I' = I ............Ans##
(c) 兩邊對 I做微分,其餘視為常數
dR/dI = ( 1/ I - 0 )/ ln 10 = 1/ ln 10 *I .........Ans##
題目不難,只是要把觀念弄清楚補比較重要,加油吧..............^^....
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.114.212.82
1F：推 artaniss:感謝喔^^可是第二題答案給１０的R次方耶? 163.25.118.38 01/06
2F：推 dunerx0712:是嘛,可是題目好像是說R要兩倍,理論上答案 140.114.212.82 01/06
3F：→ dunerx0712:應該不會在出現R的變數,或是我算錯....><" 140.114.212.82 01/06