   Chapter 15.9, Problem 3E

Chapter
Section
Textbook Problem

Find the Jacobian of the transformation.3. x = s cos t, y = s sin t

To determine

To find: Jacobian transformation of x=scost and y=ssint.

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=scost.

Take partial derivative of x with respect to s to obtain xs.

xs=(1)cost

Take partial derivative of x with respect to t to obtain xt.

xt=s(sint)=ssint

Given that, y=ssint

Take partial derivative of y with respect to s to obtain ys.

ys=(1)sint

Take partial derivative of y with respect to t to obtain yt

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