Stokes's theorem一問

👨🏻‍🏫 學術台數學

2009-06-04 6:27 am

wiki寫:

The integral of the curl of a vector field over a surface equals the line integral of the vector field over the curve bounding the surface.

我想問the curve bounding the surface係指什麼?
如果係一條(曲)線,線又點bound the surface?
如果唔係線,又點line integral?

請賜教!

更新1:

如果一個surface無底呢? 如:x^2+y^2+z^2=1 仲有,個底係唔係一定要平? 還是它的意思是投影?

更新2:

感謝maximal_ideal_space 的意見, 還有的問題是:個底係唔係一定要平? 一個斜的底可否接受?如x+y-z=0

回答 (2)

2009-06-04 6:37 am

✔ 最佳答案

The integral of the curl of a vector field over a surface equals the line integral of the vector field over the curve bounding the surface.

圖片參考：http://tbn1.google.com/images?q=tbn:rdNVSlwuh_QiQM:http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem_files/image001.gif

圖片參考：http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem_files/empty.gif

如圖所示﹐每一個空間中的surface必定有一個底﹐那個底會被一條curve包圍住。參考
http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx

圖片參考：http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem_files/empty.gif

2009-06-05 15:07:11 補充：
一個斜的底可否接受?如x+y-z=0

可以

參考: http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx

👍 0 👎 0

2009-06-04 6:25 pm

無底的話，boundary就是empty，這時line integral = 0.

👍 0 👎 0

收錄日期: 2021-04-26 13:38:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090603000051KK01807

檢視 Wayback Machine 備份