Explanation Given: The given equation are, x = 4 u − v y = 4 v − w and z = u + w And ∂ ( x , y , z ) ∂ ( u , v , w ) = | ∂ x ∂ u ∂ x ∂ v ∂ x ∂ w ∂ y ∂ u ∂ y ∂ v ∂ y ∂ w ∂ z ∂ u ∂ z ∂ v ∂ z ∂ w | Formula used: The Partial differentiation : If f = x y + 1 Then ∂ f ∂ x = y Determinant is calculated as: Δ = | a b d c | = a c − b d Calculation: To find the value of Jacobian ∂ ( x , y , z ) ∂ ( u , v , w ) = | ∂ x ∂ u ∂ x ∂ v ∂ x ∂ w ∂ y ∂ u ∂ y ∂ v ∂ y ∂ w ∂ z ∂ u ∂ z ∂ v ∂ z ∂ w | By putting the value of x , y , z Thus we get, ∂ ( x , y , z ) ∂ ( u , v , w ) = | ∂ ( 4 u − v ) ∂ u ∂ ( 4 u − v ) ∂ v ∂ ( 4 u ȡ

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Author: Larson

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Chapter 14.8, Problem 36E

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To calculate: The value of the Jacobian ∂(x,y,z)∂(u,v,w) where, x=4u−vy=4v−w and z=u+w.

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Chapter 14.8, Problem 35E

Chapter 14.8, Problem 37E

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Chapter 14 Solutions

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The value of the Jacobian ∂ ( x , y , z ) ∂ ( u , v , w ) where, x = 4 u − v y = 4 v − w and z = u + w .

Solution Summary: The author calculates the value of the Jacobian partial '(x,y,z)', where x = 4u-v, y=4v-w

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To calculate: The value of the Jacobian ∂(x,y,z)∂(u,v,w) where, x=4u−vy=4v−w and z=u+w.

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Chapter 14 Solutions