   Chapter 15.9, Problem 2E

Chapter
Section
Textbook Problem

Find the Jacobian of the transformation.2. x = u2 + uv, y = uv2

To determine

To find: Jacobian transformation of x=u2+uv and y=uv2.

Explanation

Definition used: Jacobian transformation

The Jacobian of the transformation T given by x=g(u,v) and y=h(u,v) is

(x,y)(u,v)=|xuxvyuyv|=xuyvxvyu

Calculation:

Given that, x=u2+uv.

Take partial derivative of x with respect to u to obtain xu.

xu=2u+v(1)=2u+v

Take partial derivative of x with respect to v to obtain xv.

xv=u(1)=u

Given that, y=uv2

Take partial derivative of y with respect to u to obtain yu

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