This preview shows page 1. Sign up to view the full content.
Optics 287, Math 287
March 19, 2009
11:05 to 12:20
Midterm Exam
1.
a) Calculate the gradient, divergence or curl (whichever applies) of
A
(
r
)
=
r
n
r
,
where
n
is an integer. (15 pts.)
b) For what values of
n
is the divergence constant? (5 pts.)
c) For what values of
n
is the divergence equal to zero? (5 pts.)
d) For what values of
n
is the curl zero? (5 pts.)
e) Consider the integral of the divergence of
A
over the volume contained in a
unit sphere centered at the origin. What is the value of this integral for any
n
?
(10 pts.)
2.
(15 pts) Consider the function
f
(
x
)
=
1
−
x
,
0
≤
x
<
1,
−
1
−
x
,
−
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 alonso

Click to edit the document details