3.7 .
Surface e flux integral
surface integral notation :
µ real valued function defined
1- f- ds if f- is a
-
on S
E:
2.
fg E. d5 •
F- :
vector field defined on s
¥
FLUX :S:-.
eÑR ÷: ÷
◦ Divide big surface into sillier surfaces
§
approximate area
*ⁿmf} §
' d'
◦ If f-Guy/ 2-1=1 surface
, integral becomes
[ f- fully .tl gives density mass of
,
5=1,1 fds
determine Hds ?
How do we
µ fishy ,
Depends on how surface described .
1. S a parametric surface
J FCUN)
:
cxlu , v1, ylu , v7 2- ( UN) > ( un ) C- D
=
,
fl≥ lyitlds
Y SSFCFCUND / Fuxirvld A
:
b ↳ magnitude / length
?⃝
, Replace 2- with
2. S :
2- =
gloiiy ) →
tf tiny 94491 )Vgx , DA
b
↳ of sin
projection XY plane
-
.
example part of plane 2
1. Determine etds with S 21--144442
µ
✗ : V -
I≤ u≤ o
Y
'
214 " "
◦ ≤ ✓ ≤ I
parametric eq given 3134
.
2- = -
v
① Partial derivatives ↓
Fcuiv)
run
Fu <
1,37
-
4,
_
Fv =
< 2,1 , -17
/ Ful =
✓Ñ
surface integral
① If [( 1-144124^13134 -
V)
]✓ÑdA
b
=/ ! /! ,
Guava 4) Ñdvd4
=✓Ñ
,
Surface e flux integral
surface integral notation :
µ real valued function defined
1- f- ds if f- is a
-
on S
E:
2.
fg E. d5 •
F- :
vector field defined on s
¥
FLUX :S:-.
eÑR ÷: ÷
◦ Divide big surface into sillier surfaces
§
approximate area
*ⁿmf} §
' d'
◦ If f-Guy/ 2-1=1 surface
, integral becomes
[ f- fully .tl gives density mass of
,
5=1,1 fds
determine Hds ?
How do we
µ fishy ,
Depends on how surface described .
1. S a parametric surface
J FCUN)
:
cxlu , v1, ylu , v7 2- ( UN) > ( un ) C- D
=
,
fl≥ lyitlds
Y SSFCFCUND / Fuxirvld A
:
b ↳ magnitude / length
?⃝
, Replace 2- with
2. S :
2- =
gloiiy ) →
tf tiny 94491 )Vgx , DA
b
↳ of sin
projection XY plane
-
.
example part of plane 2
1. Determine etds with S 21--144442
µ
✗ : V -
I≤ u≤ o
Y
'
214 " "
◦ ≤ ✓ ≤ I
parametric eq given 3134
.
2- = -
v
① Partial derivatives ↓
Fcuiv)
run
Fu <
1,37
-
4,
_
Fv =
< 2,1 , -17
/ Ful =
✓Ñ
surface integral
① If [( 1-144124^13134 -
V)
]✓ÑdA
b
=/ ! /! ,
Guava 4) Ñdvd4
=✓Ñ
,
