Summary: 1. The general transformation formula.
Theorem 1.1. Suppose
(i) k and n are integers and 1 k n;
(ii) A is a closed and bounded subset of Rk
;
(iii) F : A Rn
and
(a) F is one-one;
(b) F has a continuously differentiable extension to an open set containing
A;
(iv) g : F[A] R and g is continuous.
Then
F[A]
g =
A
(g F) JF
where, for each x A,
JF(x)
is the square root of the sum of the squares of the determinants of the n
k k by k

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

Collections: Mathematics