Re: Off Topic - Jacobian and Change of Variables
- To: mathgroup at smc.vnet.net
- Subject: [mg35876] Re: [mg35859] Off Topic - Jacobian and Change of Variables
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Mon, 5 Aug 2002 06:01:43 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
You should be able to find this in every book which deals with integration on manifolds. The first one I looked at is Michael Spivak's short and elegant undergraduate text "Calculus on manifold"(1965 edition) which has the proof on page 67. Andrzej Kozlowski On Sunday, August 4, 2002, at 07:00 PM, Kevin J. McCann wrote: > 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 > > > > >