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 Green's theorem.
let c be a orientated piecewise smooth
close# curve in XY plane that forms the
-
boundary of a
Region R :
@
④
, Then :
{ Pdx Ady If an Pydn
-
. _
-
R
or alternatively
{ F. di
JI Qu
Py DA f- P a >
with
- - = -
,
R
③ different ways to determine
{ F- di with Cin R2 :
-
c ( Lu 3. 2)
1. Parametrize the curve
C : FC 1- 5- < ✗ It)
, yet ) >
,
t E ca b
, ]
{ E. OF
-
-
Jab Écrct) ) F -
'
Lt) dt
theorem of line integrals if
2. Fund .
F- =
conservative v. f. that is F- =D f-
then
{ E. di Tf f- ( Fcb) ) f- ( F (d) )
= = -
Green 's theorem if [ is closed csimp e)
3.
/
curve , orientated counter clock -
.
Spd ≥ ' Qdy F- di
{ J) an byd A ICU 3. 4)
- -
-
-
R
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