   Chapter 15.9, Problem 4E

Chapter
Section
Textbook Problem

Find the Jacobian of the transformation.4. x = peq, y = qep

To determine

To find: Jacobian transformation of x=peq and y=qep.

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=peq.

Take partial derivative of x with respect to p to obtain xp.

xp=(1)eq=eq

Take partial derivative of x with respect to q to obtain xq.

xq=p(eq)=peq

Given that, y=qep

Take partial derivative of y with respect to p to obtain yp.

yp=q(ep)=qep

Take partial derivative of y with respect to q to obtain yq

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