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Unformatted text preview: Time t (sec) 0 0.5 1.5 Position x (m) 0 1 1.7 Question 4. a) Consider x x f 2 sin ) ( = . Find the exact value of 1 = x dx df b) Sketch ) ( x f to verify that 15 . = Δ x is a reasonable grid spacing here. With 15 . = Δ x , estimate 1 = x dx df using first, second and third order forward differences. (c) Try a first order forward difference with 05 . = Δ x and . 005 . = Δ x Question 5. a) Sketch the function x e y x f y cos 3 ) , ( 2 − = for 2 / π ≤ ≤ x and 3 ≤ ≤ y b) Find the exact values of x f ∂ ∂ , y f ∂ ∂ , and 2 2 x f ∂ ∂ at ( 1 , 1 = = y x ) c) From (a), verify that 1 . = Δ = Δ y x is a reasonable grid spacing for this function. Estimate x f ∂ ∂ , y f ∂ ∂ , and 2 2 x f ∂ ∂ at ( 1 , 1 = = y x ) using second order, central difference formulas....
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This note was uploaded on 09/16/2011 for the course ME 303 taught by Professor Serhiyyarusevych during the Spring '10 term at Waterloo.
 Spring '10
 SerhiyYarusevych

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