作者weisl (好倫~)
看板NTU-Exam
標題[試題] 99下 黃漢水 微積分甲下 第八次小考
時間Thu Jun 16 09:54:10 2011
課程名稱︰微積分甲下
課程性質︰必修
課程教師︰黃漢水
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰100/06/14
考試時限（分鐘）：40分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題：
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一、Let Ｆ(x,y,z)= 2y cosz ｉ + e^x sinz ｊ + xe^y ｋ and S is the hemisphere
x^2 + y^2 + z^2 = 16 , z≧0 , oriented upward. (30%)
→
Find the integral ∫∫ curl Ｆ‧dＳ. [Hint: use Stokes' Theorem]
S
→ → → →
二、Let Ｆ(x,y,z)= x^4 ｉ - x^3 z^2 ｊ + 4xy^2 z ｋ and S is the surface
of the solid bounded by the cylinder x^2 + y^2 = 1 and the planes
z = x + 2 and z = 0, with outward orientation.
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(1) Find div Ｆ . (10%)
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(2) Find the integral ∫∫ Ｆ‧dＳ. [Hint: use Divergence Theorem]
S
→ → → →
三、Let Ｆ(x,y,z)= 2x^2 y ｉ + 2xy^2 ｊ + 4xyz ｋ and S is the surface
of the tetrahedron bounded by the four plane x = 0, y = 0, z = 0
and x + 2y + z = 2, with outward orientation.
→
Find the integral ∫∫ Ｆ‧dＳ. [Hint: use Divergence Theorem] (30%)
S
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