u-curves & v-curves
Let u = f ( x, y ) and v = g ( x, y ) .
So u-curves are curves in the xy-system where
u = c ( vertical lines in the uv-system ) f ( x, y ) = c
( Some curves in the xy-system)
And v-curves are curves in the xy-system where
v = c ( horiz
Two Dimensional Vector Fields
Let M:! 2 ! with z = M ( x, y ) being the correspondence
and N:! 2 ! with z = N ( x, y ) being the correspondence.
So a two-dimensional Vector Field is:
!"
!"
"
"
F:# 2 E2 with F ( x, y ) = M ( x, y ) , N ( x, y ) = M ( x, y
Math 252 Quiz #18 solutions [Instructor Teegarden]
3
9 x2
3
9 x2
[15 pts] 1. Use cylindrical coordinates to evaluate:
9 x2 y 2
0
x2dzdydx
z
9
y
Q
3
x 2+ y 2 = 9
-3
-3
y
3
x
3
x
Proj x y(Q)
3
First: dV = rdzdrd
So
3
9x2
3
9x2
Set Up
=
9r 2
0
0
0
[r