26 lines
905 B
TeX
26 lines
905 B
TeX
\documentclass{article}
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\begin{document}
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\begin{center}
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\section*{Project 2}
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Math 400, Spring 2025 \\
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Due Wed 05/07 \\
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Uzair Hamed Mohammed
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\end{center}
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\begin{enumerate}
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\item[1.] This is a problem on Gaussian quadrature and related things.
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\begin{enumerate}
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\item[a.] Explain the principle of the Gaussian quadrature.
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\item[b.] Show that the Gaussian quadrature \(\int_{-1}^{1}
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f(x) dx = c_0 f(x_0) + c_1 f(x_1)\) can be exact for all
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polynomials of degree 3 with 2 points \(x_0 = -
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\frac{1}{\sqrt{3}}\) and \(x_1 = \frac{1}{\sqrt{3}}\). Find
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\(c_0\) and \(c_1\) as well.
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\item[c.] Determine the values of \(c_i\) and \(x_i, i = 0, 1\)
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so that the quadrature formula \(\int_{-1}^{1} x^2 f(x) dx =
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c_0 f(x_0) + c_1 f(x_1)\) will be exact for all polynomials of degree 3.
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\end{enumerate}
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\end{enumerate}
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\end{document}
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