Chapter 14, Problem 72RE

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Finding a JcobianIn Exercises 71–74, find the Jacobian ∂ ( x , y ) / ∂ ( u , v ) for the indicated change of variables. x = u 2 + v 2 ,     y = u 2 − v 2

To determine

To calculate: The Jacobian (x,y)(u,v) for the indicated change in variables x=u2+v2 and y=u2v2.

Explanation

Given:

The value of x=u2+v2 and value of y=u2âˆ’v2.

Formula used:

Jacobian âˆ‚(x,y)âˆ‚(u,v)=âˆ‚xâˆ‚uâˆ‚yâˆ‚vâˆ’âˆ‚yâˆ‚uâˆ‚xâˆ‚v

Calculation:

Taking the given equation:

x=u2+v2y=u2âˆ’v2

The definition of Jacobian implies that:

âˆ‚(x,y)âˆ‚(u,v)=|âˆ‚xâˆ‚uâˆ‚xâˆ‚vâˆ‚yâˆ‚uâˆ‚yâˆ‚v|=âˆ‚xâˆ‚uâˆ‚yâˆ‚vâˆ’âˆ‚yâˆ‚uâˆ‚xâˆ‚v

In above equation we substitute the value of x and y

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