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Card 10 / 13:
Jacobian
the Jacobian J ( u , v ) in two variables is a 2 × 2 determinant: J ( u , v ) = | ∂ x ∂ u ∂ y ∂ u ∂ x ∂ v ∂ y ∂ v | ; the Jacobian J ( u , v , w ) in three variables is a 3 × 3 determinant: J ( u , v , w ) = | ∂ x ∂ u ∂ y ∂ u ∂ z ∂ u ∂ x ∂ v ∂ y ∂ v ∂ z ∂ v ∂ x ∂ w ∂ y ∂ w ∂ z ∂ w |
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