line (and optional surface) integrals
line integrals
Lecture notes on scalar line integrals
Lecture notes on vector line integrals
summary
[worksheet:
intscalarsemicircle.mw
, short:
lineintplane.mw
]
Lecture Notes on conservative vector fields
"antidifferentiation" in multivariable calculus: potential function for conservative vector field;
Exercise:
lineintvec.pdf
(inverse square vector fields)
Lecture Notes on Green's Theorem
[
s16-4.mw
]
Lecture Notes on grad, div, curl
divergence and curl, Gauss and Stokes versions of Green's Theorem;
interpretation of circulation and flux densities for curl and div [
divcurl.mw
]
inverse power radial force fields:
divinversep.pdf
surface integrals (optional)
Lecture Notes on surface integrals and Gauss and Stokes
[
flux motivation: sunshine on
Earth surface
and
seasons
;
Maxwell's eqns
]
[
example1
: surface area and centroid of
hemisphere
, Gauss law example, wedge of cylinder 16.7.example3;
example2
: parabola of revolution (
Stewart16.7.23
expanded into Gauss/Stokes examples)].
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