# 实用物理和计算2| Practical Physics and Computing 2代写PHAS00029代考

\begin{gathered}
m=\frac{\sum_{i} w_{i} \sum_{i} w_{i} x_{i} y_{i}-\sum_{i} w_{i} x_{i} \sum_{i} w_{i} y_{i}}{\sum_{i} w_{i} \sum_{i} w_{i} x_{i}^{2}-\left(\sum_{i} w_{i} x_{i}\right)^{2}} \
\alpha_{m}=\sqrt{\frac{\sum_{i} w_{i}}{\sum_{i} w_{i} \sum_{i} w_{i} x_{i}^{2}-\left(\sum_{i} w_{i} x_{i}\right)^{2}}}
\end{gathered}

\begin{aligned}
c &=\frac{\sum_{i} w_{i} x_{i}^{2} \sum_{i} w_{i} y_{i}-\sum_{i} w_{i} x_{i} \sum_{i} w_{i} x_{i} y_{i}}{\sum_{i} w_{i} \sum_{i} w_{i} x_{i}^{2}-\left(\sum_{i} w_{i} x_{i}\right)^{2}} \
\alpha_{c} &=\sqrt{\frac{\sum_{i} w_{i} x_{i}^{2}}{\sum_{i} w_{i} \sum_{i} w_{i} x_{i}^{2}-\left(\sum_{i} w_{i} x_{i}\right)^{2}}}
\end{aligned}

## PHAS00029 COURSE NOTES ：

$$\begin{array}{r} f\left(x_{1}+h\right) \approx f\left(x_{1}\right)+f^{\prime}\left(x_{1}\right) h, \ \therefore f\left(x_{1}\right)+f^{\prime}\left(x_{1}\right) h \approx 0, \ \therefore h \approx-\frac{f\left(x_{1}\right)}{f^{\prime}\left(x_{1}\right)} . \end{array}$$
This allows us to write down a second approximation to the zero crossing:
$$x_{2}=x_{1}-\frac{f\left(x_{1}\right)}{f^{\prime}\left(x_{1}\right)} .$$
The process can be repeated to obtain successively closer approximations. If after $s$ iterations the approximate solution is $x_{s}$ then the next iteration is $x_{s+1}$, and these quantities are related via the relation:
$$x_{s+1}=x_{s}-\frac{f\left(x_{s}\right)}{f^{\prime}\left(x_{s}\right)} .$$