作者weisl (好伦~)
看板NTU-Exam
标题[试题] 99下 黄汉水 微积分甲下 第八次小考
时间Thu Jun 16 09:54:10 2011
课程名称︰微积分甲下
课程性质︰必修
课程教师︰黄汉水
开课学院：工学院
开课系所︰土木工程学系
考试日期（年月日）︰100/06/14
考试时限（分钟）：40分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题：
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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%)
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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
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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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