課程名稱︰微積分甲下
課程性質︰必修
課程教師︰薛克民
開課學院：電資學院、工學院、管理學院
開課系所︰電機系、資工系、材料系、資管系
考試日期（年月日）︰100/6/13
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 :
1. Apply Green's theorem to find the area of the region bounded by the curve
parametrized by r(t) = ( cos(t), [sin(t)]^3 ), 0 ≦ t ≦ 2π. (10%)
→ → → →
2. Find the circulation of the field Ｆ = -(x^2)y ｉ + x(y^2) ｊ + (z^2) ｋ
around the curve C in which the circular cylinder (x^2) + (y^2) = 2x
meets the cone z = 2√[(x^2) + (y^2)] counterclockwise as viewed above.
(10%)
3. Evaluate the integral (10%)
∫∫ y ds
S
where S is the surface z = x + (y^2), 0 ≦ x ≦ 1, 0 ≦ y ≦ 2
→ → →
→ z ｉ + y ｊ + x ｋ
4. Find the flux of the vector field Ｆ(x,y,z) = ─────────────
(x^2 + y^2 + z^2)^(3/2)
over the unit sphere (10%)
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※ 編輯: rod24574575 來自: 218.167.193.80 (06/28 13:58)