Explanation G is a coordinate transformation from x y -plane to u v -plane then G ( u , v ) = ( x , y ) ---------------- (i) Given: G ( u , v ) = ( u e v , e u ) ---------- (ii) Comparing (i) and (ii), x = u e v ; y = e u Calculation: Jacobian of the transformation is J ( u , v ) = ∂ ( x , y ) ∂ ( u , v ) = | ∂ x ∂ u ∂ x ∂ v ∂ y ∂ u ∂ y ∂ v | --------- (iii) Where ∂ x ∂ u , ∂ x ∂ v , ∂ y ∂ u , ∂ y ∂ v are first order partial derivatives. ∂ x ∂ u = ∂ ∂ u ( u e v ) = e v ∂ ∂ u ( u ) = e v ( 1 ) = e v [While differentiating partially with respect to u treat v as constant] ∂ x ∂ ...

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Chapter 16.6, Problem 18E

To determine

The Jacobian

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Chapter 16.6, Problem 17E

Chapter 16.6, Problem 19E

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S (sechu + tanh u)² du

Compute the Jacobian at the indicated point. (5.증) G(r, t) = (r sin (t), r – cos (t)), (r, t) = (Express numbers in exact form. Use symbolic notation and fractions where needed.) Jac(G) (5. 증) =

Please help find u(x,t)

Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The Jacobian

Solution Summary: The author explains that the Jacobian solution is J = e u + v.

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Chapter 16 Solutions