2D Jacobian

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Let , be a transformation of the - plane into the - plane. Let be a small rectangle with sides parallel to the and axes with side lengths and . The image of this rectangle in the - plane is a curved rectangle . The coordinates of these points are:

[more]

,

,

,

.

These points can be approximated by the points of the parallelogram

,

,

,

.

The area of this parallelogram is the absolute value of

.

The last determinant is called the Jacobian and is usually denoted by .

[less]

Contributed by: Izidor Hafner (October 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference

[1] E. J. Borowski and J. M. Borwein, Collins Dictionary of Mathematics, New York: Collins, 1989 p. 314.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send