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lecture10 - MATH 100 Lecture 10 Total Differential Total...

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2006 Fall MATH 100 Lecture 10 1 MATH 100 Lecture 10 Total Differential ( ) ( ) ( ) ( ) ( ) ( ) Total Differential: Consider , , , Define total differential as , , , , , , while the increment is Δ , , , , If is diff., then x y z w f x y z dw f x y z dx f x y z dy f x y z dz w f x x y y z z f x y z f w = = + + = + Δ + Δ + Δ Δ = ( ) ( ) 1 2 3 1 2 3 , , 0 as , , 0,0,0 dw x y z x y z ε ε ε ε ε ε + Δ + Δ + Δ Δ Δ Δ
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2006 Fall MATH 100 Lecture 10 2 MATH 100 Lecture 10 Total Differential Ex: Length, width & height of a box are measured with an error of at 5%, when they are used to calculate the diagonal, what is the maximal percentage error? ? know want to we % 5 Given : diagonal the of Length : Solution 2 2 2 Δ + + = D D z Δ z , y Δ y , x Δ x z y x D
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