/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 60 Let 惟聽and 惟'聽be subsets of R... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Q. 60 (page 1080)

Let 惟and 惟'be subsets of R2. Use the results of Exercise 59 to prove that if a transformation T:惟鈫�惟'is invertible, and if both T and T-1are differentiable, then role="math" 鈭�(x,y)鈭�(u,v)鈭�(u,v)鈭�(x,y)=1.

Short Answer

Expert verified

It is proved that鈭�(x,y)鈭�(u,v)鈭�(u,v)鈭�(x,y)=1.

Step by step solution

01

Given information

Consider a chain of functions is defined as,

x=x(u,v);y=y(u,v)u=u(s,t);v=v(s,t)

The chain rule of Jacobian is defined as,

role="math" 鈭�(x,y)鈭�(u,v)鈭�(u,v)鈭�(s,t)=鈭�(x,y)鈭�(s,t)

02

Proof

Consider a transformation T:(x,y)鈫�(u,v)andT-1:(u,v)鈫�(x,y).

Use the above-given definition of the chain rule of Jacobians to derive the relation.

鈭�(x,y)鈭�(u,v)鈭�(u,v)鈭�(x,y)=鈭�(x,y)鈭�(x,y)=1

Hence, proved.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�03鈭�01-y/3鈭�02-(2/3)y-2zf(x,y,z)dxdzdy

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�-33鈭�-9-z29-z2鈭�03-x2+z2f(x,y,z)dydxdz

Expressthesum3e4+3e9+3e16+4e4+4e9+4e16usingdouble-summationnotation.

Evaluate the sums in Exercises 23鈥�28.

鈭�i=14鈭�j=13鈭�k=12ij2k3

In Exercises 45鈥�52, rewrite the indicated integral with the specified order of integration.

Exercise 42 with the order dy dx dz.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.