# hw10 - ASE 311 Engineering computation Fall 2009 Homework...

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Unformatted text preview: ASE 311 Engineering computation, Fall 2009, Homework 10 Due: Friday, November 20, 2:00 PM in the lecture room JGB 2.216 Report all work, including any m-ﬁles you have written. You may also ﬁnd the command diary useful in recording your MATLAB session. Please write clearly and be sure to label for which problem each solution is. Please, staple Part I and Part II separately and make sure that your name is written on both parts. Part I 1. [Gauss rule] Evaluate the vertical distance travelled ⎧ ( ) = 11 2 − 5 ⎨ ( ) = 1100 − 5 ⎩ ( ) = 50 + 2( − 20)2 Use an exact Gauss-Legendre rule for each interval. by a rocket when its vertical velocity is 0 ≤ ≤ 10 10 ≤ ≤ 20 20 ≤ ≤ 30 2. [Three-point Gauss-Legendre rule] Verify that the three-point quadrature formula 1 ( )d ≈ −1 1 9 5 − 3 5 + 8 (0) + 5 3 5 (1) is exact for polynomials of order ﬁve. Part II 3. Apply the quadrature rule (1) to the computation of 2 exp(− 2 ) d 0 4. Evaluate the double integral 1 −1 0 2 ( 2 −2 2 + 3 )d d (a) using two-point Gauss Legendre rule in both directions (b) using the MATLAB built-in function dblquad 5. Use centered diﬀerence approximations to estimate the ﬁrst and second derivatives of at = 2 for ℎ = 0.1. Employ (ℎ2 ) formulas for your estimates. = ...
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