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University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg35

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009

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Mtg 35: Thurs, 12Nov09


Gauss Legendre quadrature (numerical integration}

Quadrature; QUAD-->quadrilateral-->Greek: measuring areas



Area Quadrilaterals

Cubature; CUBE; Volume cubes



with the roots for , where n is the degree of and being the weight


(1)



(2)

where j=1,2,...,n

(3)

for

Ex: (2 point interpolation)

Eq.(3) P.31-3



Eq.(4) P.31-3




HW: verify table for Gauss Legendre quadrature in wikipedia, analytical expression of and and (n=integration points) after verifying the expression for with ; (see HW p31-3 )

Evaluate numerically and and compute results with Abram & Stegum (see lecture plan)

Question: How does Gauss Legendre quadrature compare to other quadrature methods, e.g. trapezoidal rule?

Answer: Look at , Eq.(3) P.35-2. Consider ...

References

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