課程名稱︰微積分甲下
課程性質︰數學系大一必帶
課程教師︰陳榮凱
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/05/22
考試時限（分鐘）：30
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
The total is 25 points.
(1) (10 pts) Assume that both f, g has continuous second partial derivative. S
3
is a bounded surface in R with piecewise smooth boundary C = ∂S. Prove
→
that ∫( f ▽g + g ▽f )．T dt = 0.
→ 2
(2) (15 pts) Verify Divergence Theorem for F = ( x , xy, z ), and E is the
2 2
solid bounded by the paraboloid z = 4 - x - y that lies above z = 3.