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Assignment#4 - MA 202 Numerical Methods in Engineering...

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MA 202 Numerical Methods in Engineering Assignment # 4 (Due by: Friday, February 14 th 2014) 1. Use the Trapezoidal rule to obtain the approximate value for n=1, 2, 4 of the following integral (n represents number of segments/intervals): (10 Marks) 2. Use Simpson’s 1/3 and 3/8 rules to find the integral given in the problem 1. (10 Marks) 3. Degree of Precision: Let I n be a quadrature rule, and assume it is exact for all polynomials of degree ≤ p . Then we say that I n has degree of precision p . You can find degree of precision of a quadrature rule by calculating integrals of p+1 monomials as follows: e.g. The 2-point Gauss Legendre formula given by ( ) ( ) has degree of precision p=3 as it will give exact results for monomials: . Now calculate the degree of precision of the following quadrature formula: (10 Marks) 4. The quadrature formula is exact for all polynomials of degree less than or equal to 2. Determine c 0 , c 1 and c 2 . What is the degree of precision of this formula? (10 Marks) 5. Bound the error in
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