这是一份ed.ac爱丁堡格大学MATH11147作业代写的成功案

$$
R_{t_{3}}=\frac{d c_{l}}{d u_{j}}=\frac{\partial c_{i}}{\partial u_{j}}+\sum_{k=1}^{n} \frac{\partial c_{i}}{\partial X_{k}} \frac{d X_{k}}{d u_{j}}
$$
We can now write in the form $R^{T} R \delta u=-R^{T} c$. This is cquivilent to the least squares problem MIN $|R \mathcal{x}+c|_{2}$ which can be solved by applying a constrained linear least squares solver.

The test coses discussed in this section are pressure matching cases inwolving a target pressure distribution obtained by analyzing an airfoll section similar to the ONERA M6 section. The initial airfoal was the NACA0012. The objective function is
$$
I=\frac{1}{2} \sum_{l=1}^{q} W_{k}\left[\left(c_{\mathrm{p}}\right){\ell}-\left(c{p}\right)_{1}\right]^{2}
$$

MATH11147  COURSE NOTES ：

$$
\beta(x)=\frac{\phi_{h}(x)}{\phi_{j o}(x)}
$$
and onstruct the linear approximation
$$
\beta_{k}(x)=\beta\left(x_{k}\right)+\nabla \beta\left(x_{k}\right)^{T}\left(x-x_{k}\right) .
$$
Then
$$
\bar{\phi}(x)=\beta_{k}(x) \phi_{l o}(x)
$$