lecture10

Lecture10 - MATH 100 Lecture 10 Total Differential Total Differential Consider w = f x y z Define total differential as dw = f x x y z dx f y x y z

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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 xyz wf x y z dw f x y z dx f x y z dy f x y z dz x x y y z z f x y z f w = =++ =+ Δ + Δ + Δ Δ= ( ) 123 , , 0 as , , 0,0,0 dw x y z εε ε εεε + Δ →Δ Δ Δ
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
2006 Fall MATH 100 Lecture 10 3 MATH 100 Lecture 10 Total Differential 22 2 2 2 222 2 2 2 2 2 max , , 0.05 Dd D DD xyz dx dy dz xd x y dy zd z x y zx x y z y x y zz d x d y d z x y z Δ =++ ++ ⎛⎞ ⎜⎟ ⎝⎠ ⎧⎫ = ⎨⎬ ⎩⎭
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2006 Fall MATH 100 Lecture 10 4 MATH 100 Lecture 10 Total Differential Ex: ( ) ( ) () ? 1 2 3 find you can 5 1 2 3 and 2 . 1 , 2 , 5 1 , 2 , 3 Given , ,- f , ,- f // u f D u = = G G Sol: ( ) ( )
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

Page1 / 7

Lecture10 - MATH 100 Lecture 10 Total Differential Total Differential Consider w = f x y z Define total differential as dw = f x x y z dx f y x y z

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online