[試題] 104-1 張書瑋 工程數學一 第四次小考
課程名稱︰工程數學一
課程性質︰土木系大二必修
課程教師︰張書瑋
開課學院：工學院
開課系所︰土木系
考試日期（年月日）︰2015.12.28
考試時限（分鐘）：50分鐘
試題 :
Engineering Mathematics (I) Quiz 4
1. (15%)Find a normal vector for hyperbolic cylinder x^2 - y^2 = 1.
2. (30%)Evaluate ∫F(r) dr counterclockwise around the boundary C of the region
c
R by Green's Theorem, F = [x^2 e^y , y^2 e^x], R the rectangle with vertices
(0,0),(2,0),(2,3),(0,3)
3. (25%)Evaluate ∫F(r) dr for the given data. F = [xy,x^2 y^2], C the quater-
c
circle from (2,0) to (0,2) with center (0,0), show the details.
4. (30%)Evaluate the surface intergal ∫∫F‧n dA by the divergence theorm.
s
F = [e^x,e^y,e^z], S the surface of the cube |x| < 1 , |y| < 1 , |z| < 1.
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