作者steve1012 (steve)
看板NTUBIME103HW
标题[微积分] 17.7 46题
时间Sat Jun 18 16:45:57 2011
好像很多人不会算
这题不要直接做太麻烦了
以下是jacobian的算法
set x=au y=bt z=cv
the the original ellipsoid can transfer to a sphere
2 2 2
u + y + z =1
我用p代表partail的符号
partial(x,y,z) | px/pu px/pt px/pv |
J = -------------------- = | py/pu py/pt py/pv |
partial(u,t,v) | pz/pu pz/pt pz/pv |
| a 0 0 |
= | 0 b 0 | = abc
| 0 0 c |
so ∫∫∫ dzdydx = ∫∫∫ |J|dudtdv
= ∫∫∫ abcdudtdv = abc ∫∫∫dudtdv
transfer to sphere coordinate
2π π 1 2
=abc ∫ ∫ ∫ r sinφdr dφdθ
0 0 0
it's obvious that the result of the integration is the volume of a sphere
which is 4π/3 so multiply by abc we have the volume of ellipsoid
4
= --- πabc
3
if there is any more question
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1F：推 sky2857:推 06/18 19:31
2F：推 randysuen:我觉得STEVE很厉害耶 06/18 19:56
3F：推 joe321pig:我觉得RANDY很低能耶 06/18 22:58
4F：推 yangwen5301:神手已经念到十八章了？？？ 06/19 09:29
5F：→ steve1012:18是什麽？？我念令一本所以步清楚喔 06/19 09:51
6F：→ andrew801222:某天我看到神手已经在念高等微积分了 06/19 11:14
7F：推 stan999950:我已经强到太空去了,Steve则是在异次元 06/19 14:18
8F：推 phishingphi:也可以先积z再变成omega xy是椭圆 06/19 18:52
9F：→ phishingphi:在令x=arcos theta y=brsin theta 06/19 18:52
10F：→ phishingphi:dxdy= abr r drd theta 06/19 18:53