ABSTRACT
If Z = f ( u , v , w , … ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq3682.tif"/> and δu, δv, δw, … https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq3683.tif"/> denote small changes in u, v, w,… respectively, then the corresponding approximate change δZ in Z is given by: () δ Z ≈ ∂ Z ∂ u δ u + ∂ Z ∂ v δ v + ∂ Z ∂ w δ w + … … https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq3684.tif"/>
Application: If the modulus of rigidity G = ( R 4 θ ) / L https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq3685.tif"/> , where R is the radius, θ the angle of twist and L the length, find the approximate percentage error in G when R is increased by 2%, θ is reduced by 5% and L is increased by 4%
