WTW258: LU 3.3 : THE FUNDAMENTAL THEOREM FOR LINE INTEGRALS 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 Fundamental Theorem for Line integrals.
let c be a smooth curve parametrized
differentiable fn
by Flt ), 1- c- [ dib ] ,f is a
Ofcgradient of f) is continuous oh C
defined on C and
Then final initial
f of -
di -
fifdr =
f- Crib )) -
f- ( Fla) )
The line integral 50 f. di INDEPENDENT of the
is
curve
, only the
c
initial point (Fla ) ) and the endpoint
,
( Fcb) ) are IMPORTANT
Thein between
motsoimpon-antf.is
→
the
{ f- .
di
=
flendptl-fcin.pt#opp-
potential
✓ function
To ask before applying
[Questions ] Fundamental theorem
field is conservative
?
I. HOW do we know a vector
of
How do we know v. f. defined on the curve is actually a
gradient
the fn .
É .
How do potential fn of a conservative v. f.
?
2 .
we determine _
Theorem :
<P, Q > is conservative it and only if Py=Qu
A v. f. f-
=
↓
partial
Note
:
derivatives
for vector fields in 1123 we will discuss theorem w.r.t.ie and y
in Lu 3.5 .
respectively
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