课程名称︰工程数学一
课程性质︰土木系大二必修
课程教师︰张书玮
开课学院：工学院
开课系所︰土木系
考试日期（年月日）︰2015.12.28
考试时限（分钟）：50分钟
试题 :
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.