课程名称︰微积分甲下
课程性质︰数学系大一必带
课程教师︰陈荣凯
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2014/05/22
考试时限（分钟）：30
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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.