Summary: 1. Integrals in polar coordinates.
We let
P : R2
R2
be defined by
P(r, ) = (r cos , r sin ) for (r, ) R2
.
Suppose 0 R0 < R1 < and 0 0 < 1 2 and let
A = {(r, ) : R0 r R1 and 0 1}.
Suppose
f : P[A] R
and f is Riemann integrable over P[A].
Suppose M, N are positive integers,
R0 = r0 r1 · · · rM = R1 and 0 = 0 1 · · · N = 1.
Suppose as well that
ri-1 i ri, i = 1, . . . , M, and j-1 j j, j = 1, . . . , N.
Let
S =
M
i=1

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics