   Chapter 15.9, Problem 13E

Chapter
Section
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 x2 + y2 = 1 and x2 + y2 = 2 in the first quadrant

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 x2+y2=1 and x2+y2=2 .

Calculation:

It is in polar coordinate form, by creating transformation u plays a role of r and v plays a role of θ . Therefore, x=ucosv and v=usinv .

u=x2+y2 (1)

v=tan1(yx) (2)

By substitute u and v in all the above equations to get u=1,u=2 and v=0,v=π2 .

Therefore the region of uv plane is S={(u,v)|1u2,0vπ2}

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate the definite integral. /4/4(x3+x4tanx)dx

Single Variable Calculus: Early Transcendentals, Volume I

[Type here] 22. Find the inverse of [Type here]

Mathematical Applications for the Management, Life, and Social Sciences

π does not exist

Study Guide for Stewart's Multivariable Calculus, 8th 