3310 HW#1.
Homework is graded for clarity of explanation as much as for mere
"correctness" of the final answer. You will earn partial credit much easier if
your writing is legible and organized. Please staple together your hw pages.
1.)
4
x
x
2
+
a
2
( )
3 / 2
dx
!
where ‘a’ is constant. Note that it is an indefinite integral.
2.)
d
dx
f
(
y
)
dy
1
x
!
where f(y) is a well behaved function of y
3.)
d
dx
(
y
+
x
)
dy
0
1
!
Make a quick sketch, in the xy plane, of the following vector functions.
Plot enough different vectors to get a feeling for what this field looks like in the xy plane.
4.)(a)
y
ˆ
x
(b)
r ˆ
r
(the symbol
r
here refers to the usual
r
in spherical coordinates)
(c)
x
x
2
+
y
2
ˆ
x
+
y
x
2
+
y
2
ˆ
y
(d) explain in words what plot (c) is showing?
5.) Given the scalar function T(x,y,z) (e.g. the temperature at any point in the room)
which of the three operations (div, grad, or curl) can be sensibly operated on T?
For each which can:
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 Spring '08
 POLLOCK
 Vector Calculus, Magnetism, Work, Vector field, xy plane, following vector functions, arbitrary vector function

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