   Chapter 15.9, Problem 1E

Chapter
Section
Textbook Problem

Find the Jacobian of the transformation.1. x = 2u + v, y = 4u – v

To determine

To find: Jacobian transformation of x=2u+v and y=4uv .

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|=xuyvyuxv

Calculation:

Given that, x=2u+v .

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

xu=2(1)=2

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

xv=1

Given that, y=4uv

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

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