Math6003 Hw4

The result of hw4_1_a.m:

数学HW3

The objective is to find the coefficients $(\alpha, \beta, \gamma)$ for the finite difference formula:
$$
D_{h}f(\overline{x})=\frac{\alpha f(\overline{x})+\beta f(\overline{x}-h)+\gamma f(\overline{x}-2h)}{h} \quad
$$
The analysis begins by substituting the Taylor series expansions for $f(\overline{x}-h)$ and $f(\overline{x}-2h)$ around the point $\overline{x}$ into the formula.

Homework 2= Curve Fitting

To approximate the function $$f(x) = \frac{1}{1 + \exp(4x)} $$on the interval [-5, 5], polynomial interpolation was performed using polynomials of degree n=6 and n=14. Two types of nodes were considered: equally spaced nodes and Clenshaw-Curtis nodes, the latter computed using the formula

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Part-level Dataset Available for Augmentation

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