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）︰2015.12.7
考试时限（分钟）：50 分钟
试题 :
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%)