Off Topic - Jacobian and Change of Variables
- To: mathgroup at smc.vnet.net
- Subject: [mg35859] Off Topic - Jacobian and Change of Variables
- From: "Kevin J. McCann" <kjm@KevinMcCann>
- Date: Sun, 4 Aug 2002 06:00:12 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
This problem has bothered me for years. In elementary calculus we change integration variables. For 1d this is straightforward. For 2d we make use of the cross product to determine transformed areas. For 3d we use the dot-cross product to represent a "cube" of volume. So far so good. Now when we have more than 3 we use the Jacobian determinant which is on "obvious" extension to the 3d case. I have never seen a proof of the multidimensional case. Can someone point me to a reference? Thanks, Kevin