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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6620 • Analysis of Numerical Methods II

Fall 2023 • Question 1

Question

Math 6620 • Analysis of Numerical Methods II Fall 2023 • Question 1

(Numerical Integration). Determine the coefficients \(A_0\), \(A_1\), and \(A_2\) that make the formula \[ \int _0^2 f(x)\,dx \approx A_0 f(0) + A_1 f(1) + A_2 f(2) \] exact for all polynomials of degree 3.

Raw LaTeX

(Numerical Integration).
Determine the coefficients \(A_0\), \(A_1\), and \(A_2\) that make the formula
\[
\int_0^2 f(x)\,dx \approx A_0 f(0) + A_1 f(1) + A_2 f(2)
\]
exact for all polynomials of degree 3.

Topic Tags

Numerical Differentiation and Finite Difference Operators Numerical Quadrature Polynomial Interpolation and Error Formulas Variable-Coefficient Diffusion Problems