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）︰2015.12.7
考試時限（分鐘）：50 分鐘
試題 :
Engineering Mathematics (I) Quiz 3
1. If r(t) = ( 4cost , 4sint , 5t ), find the velocity and acceleration at
point (-4 , 0 , 5π). (20%)
2. Find the volume if the vertices are (1,3,6),(3,7,12),(8,8,9) and (2,2,8).
(20%)
3. Find gradf. f= x/y.(8%)
4. Find a unit normal vctor of z - x^2 - y^2 = 0 at point P : (3,4,25).(20%)
5. f = ln(x^2 + y^2 ).Culculate ▽^2 f.(20%)
6. If v = [y , -2x , 0] is the velocity vector of a steady fluid flow. Is the
flow irrotational? Incompressible? Show the details.(12%)