WTW258: LU 3.7: THE SURFACE INTEGRAL AND FLUX INTEGRAL Lecture notes
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Course
WTW 258 - Calculus
Institution
University Of Pretoria (UP)
Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer.
These specific notes cover The surface integral and flux integrals.
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
,
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