HW1_spring09 - BIL108E...

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Unformatted text preview: BIL108E IntroductiontoScientificandEngineeringComputing Homework1 Spring09 1. Polynomial interpolation consists of determining the unique (n1) thorder polynomial that fitsndatapoints.Suchpolynomialshavethegeneralform, f (x) = p1 x n-1 + p2 x n-2 + .... + pn-1 x + pn Wherethep'sareconstantcoefficients.Astraightforwardwayforcomputingthecoefficientsis togeneratenlinearalgebraicequationsthatwecansolvesimultaneouslyforthecoefficients. Suppose that we want to determine the coefficients of the fourth order polynomial f (x) = p1 x 4 + p2 x 3 + p3 x 2 + p4 x + p5 that passes through the following five points: (200,0.746), (250,0.675), (300,0.616), (400,0.525), and (500,0.475). Each of these pairs can be sustituted intotheequationgivenabove,toyieldasystemoffiveequationswithfiveunknowns.Usethis approachtosolveforthecoefficients. 2. The Lower Colorada River consists of a series of four reservoirs as shown in the following figure.Massbalancescanbewrittenforeachreservoirandthefollowingsetofsimultaneous linearalgebraicequationsresults: 13.422 c1 750.5 0 0 0 c 0 0 -13.422 12.252 2 = 300 c3 102 0 -12.252 12.377 0 0 0 -12.377 11.797 c 30 4 Wheretherighthandsidevectorconsistsoftheloadingsofchloridetoeachofthefourlakes and , , ,and =theresultingchlorideconcentrationsforLakesPowell,Mead,Mohave andHavasu,respectively.Solvefortheconcentrationsinaechofthefourlakes. Lake Powell Lake Mead l Lake Mohave Lake Havasu Due Date: March 15, 2009 ...
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