Explanation Given: x = e u sin v , y = e u cos v Concept Used: The Jacobian is ∂ ( x , y ) ∂ ( u , v ) = ∂ x ∂ u ∂ y ∂ v − ∂ y ∂ u ∂ x ∂ v Where x = g ( u , v ) , y = h ( u , v ) Calculation: To find the Jacobian ∂ ( x , y ) ∂ ( u , v ) Where, x = e u sin v , y = e u cos v Use the formula for Jacobian ∂ ( x , y ) ∂ ( u , v ) = ∂ x ∂ u ∂ y ∂ v − ∂ y ∂ u ∂ x ∂ v For that find partial differentiation of x and y with respect to u and v , as ∂ x ∂ u = ∂ ∂ u ( e u sin v ) = e u ∂ ∂ u sin v + sin v ∂ ∂ u e u = e u ( 0 ) + sin v ( e u ) = e u sin v ∂ x ∂ v = ∂ ∂ v ( e u sin v ) = e u ∂ ∂ v sin v + sin v ∂ ∂ v e u = e u cos v + sin v ( 0 ) = e u cos v + 0 = e u

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 12.8, Problem 9PS

To determine

To find the Jacobian

∂(x,y)∂(u,v)

Where, x=eusinv,y=eucosv .

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Chapter 12.8, Problem 8PS

Chapter 12.8, Problem 10PS

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Chapter 12 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 12.1 - Prob. 1PS Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Prob. 5PS Ch. 12.1 - Prob. 6PS Ch. 12.1 - Prob. 7PS Ch. 12.1 - Prob. 8PS Ch. 12.1 - Prob. 9PS Ch. 12.1 - Prob. 10PS

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To find the Jacobian ∂ ( x , y ) ∂ ( u , v ) Where, x = e u sin v , y = e u cos v .

Solution Summary: The author explains how to find the Jacobian using the following formula: x=eumathrmsinv,

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To find the Jacobian

∂(x,y)∂(u,v)

Where, x=eusinv,y=eucosv .

Want to see the full answer?

Chapter 12 Solutions

To find the Jacobian ∂ ( x , y ) ∂ ( u , v ) Where, x = e u sin v , y = e u cos v .

Solution Summary: The author explains how to find the Jacobian using the following formula: x=eumathrmsinv,

Concept explainers

Videos

To find the Jacobian ∂(x,y)∂(u,v) Where, x=eusinv,y=eucosv .

Want to see the full answer?

Chapter 12 Solutions

To find the Jacobian

∂(x,y)∂(u,v)

Where, x=eusinv,y=eucosv .