[微積分] 17.7 46題

看板NTUBIME103HW作者steve1012 (steve)時間14年前 (2011/06/18 16:45)推噓6(6推 0噓 4→)

留言10則, 8人參與討論串1/1

好像很多人不會算這題不要直接做太麻煩了以下是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的符號 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 please call 0929208089 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 220.132.83.187

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sky2857

06/18 19:31, , 1^F

06/18 19:31, 1^F

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randysuen

06/18 19:56, , 2^F

06/18 19:56, 2^F

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joe321pig

06/18 22:58, , 3^F

06/18 22:58, 3^F