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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

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 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}

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Chapter 15 Solutions

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