Supplement to BOB
(page 6)
9.8, #13b
div
v
div
Ð0 Ñœ
Ò0@ß0@ß0@Óœ
p
"#$
`Ð0@ Ñ
`B
`C
`D
(product rule)
œ
0
@
0
0
`@
`0
"#
$
•
div v
• v
œ0
ß ß
Ò@ß@ß@Óœ0
f0
pp
Š‹
’
“
$
9.9, #6
ÒD
ß
B
ß
C
Ó
sin
sec
cos
#
9.9, #16d
curl(grad )
curl
i
j
k
0œ
œ
ppp
’“
ââ
```
œ
ß
ß
œ
!
p
’Š
‹
“
`C`D
`D`C
`B`D
`D`B
`B`C
`C`B
##
####
(as long as all partials are continuous)
10.1, #4
r
p
Ð>Ñ œ Ò#
>ß #
>Ó
! Ÿ > Ÿ
cos
sin
1
'
G
F •
r
p
.œ
p
"'
$
10.1, #8
'
!
#
>
#
"Î)
""
#%
"
#
$
’
“
cosh
sinh
sinh
cosh
>ß
Ð> Ñß /
"ß #>ß $> .> œ
/
Ð" "Ñ ¸ !Þ')&(
•
10.3, #10
''
!B
B
BC
$
BC/
.C .B œ
/
"#
'
10.4, #9
Since
F
is the gradient of a scalar function, the line integral is path independent, and
p
therefore its value around the closed curve
is zero.
G
10.5, #13
BOB's answer is correct.
Here is another correct answer.
r
N
p
Ð?ß@ÑœÒ?ß@ß
Ð"'%?#@ÑÓ
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/28/2010 for the course ESE 317 taught by Professor Hastings during the Fall '08 term at Washington University in St. Louis.
 Fall '08
 Hastings

Click to edit the document details