Chapter 15.9, Problem 13E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A region *R* in the *xy*-plane is given. Find equations for a transformation *T* that maps a rectangular region *S* in the *uv*-plane onto *R*, where the sides of *S* are parallel to the *u-* and *v*-axes.

**13.** *R* is lies between the circles *x*^{2} + *y*^{2} = 1 and *x ^{2}* +

To determine

**To find:** Equation for the transformation *T* maps with given rectangular region *S*.

Explanation

**Given:**

A region *R* in the first quadrant lies between the circles

**Calculation:**

It is in polar coordinate form, by creating transformation *u* plays a role of *r* and *v* plays a role of

By substitute *u* and *v* in all the above equations to get

Therefore the region of *uv* plane is

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