Hi every1. I am reading a book on gridding that does not prove many of the mathematical theorems that it uses. One of the theorems claims that the inverse of the jacobi matrix (defined as a matrix whose (i,j)-entry is di-x(i)/di-shi(j) is a matrix whose (i,j)-enties are given by di-shi(i)/di-x(j). I can see how the product of these matrices gives 0s for off diagonal entries but I can't prove that the elements on the main diagonal of the product are 1. Does anyone know a proof? Thx.

What is the title of the book and at any page you have problems.

your message is nt clear: di-x(i)/di-shi(j) ?? shi ??

The title of the book is "Grid Generation Methods" by Vladimir D. Liseikin, 1999, and the publisher is Springer. shi is how I pronounce the Greek letter used to label the curvilinear coordinates (the correct pronounciation may be xi?)

And the discussion is on page 32.

(1). There is a very good book on numerical grid generation, free online, by Prof. Joe Thompson, which includes a lot of math and derivations. (2). The nomenclature used is somewhat different from others, but you can pick up any advanced calculus book to help you understand these geometry related coordinate transformation. (3). Basicall, these are related to the coordinates, distance, area and volume between transformation. (between two coordinate systems) (4). (finite volume approach uses only one coordinate system, thus they bypass the basic math.) I don't have your book, so I can't help directly. Try Joe Thompson's free internet book on grid generation.

I don't find your book but I want to propose you something better.

you can write your question on "Math Forum" on http://forum.swarthmore.edu/.

Best Regards

many of the theorems used in grid transformations are to be found in your introductory calculus book. a good one is the one everybody uses here in US colleges with the violin on the cover.