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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|空气动力学代写Aerodynamics代考|Acceleration Potential

Another useful potential function which is used in aerodynamics is the acceleration potential. If we recall the momentum equation for barotropic flows:
$$\frac{D \mathbf{q}}{\mathrm{Dt}}=-\nabla \int \frac{d p}{\rho}$$
As seen in the left hand side of the equation, the material derivative of the velocity vector is obtained from the gradient of a function of pressure and density only. Hence, we can define the acceleration potential as follows
$$\frac{D \mathbf{q}}{\mathrm{D} t}=\nabla \psi \text {. }$$
As a result of last line the momentum equation reads as,
$$\nabla \psi+\nabla \int \frac{d p}{\rho}=0$$
The integral form of the last equation hecomes
$$\psi=-\int \frac{d p}{\rho}+\mathrm{F}(t)$$
The pressure term integrated at the right hand side of the equation from free stream to the point under consideration gives,

$$\psi=\frac{p_{\infty}-p}{\rho}$$
Because of the direct relation between the pressure and the acceleration potential, this potential is also called the pressure integral. Let us rewrite the Kelvin’s equation in gradient form
$$\nabla\left[\frac{\partial \phi}{\partial t}+\frac{q^2}{2}+\int \frac{d p}{\rho}\right]=0$$

## 物理代写|空气动力学代写Aerodynamics代考|Moving Coordinate System

The linearized equations which are obtained previously enable us to analyze aerodynamical problems more conveniently. Let us now elaborate on the coordinate systems which will further simplify the equations. The type of external flows we study usually considers a constant free stream velocity $U$ at the far field. The reference frame used for this type analysis is a body fixed coordinate system which moves in the negative $x$ direction with velocity $U$. Another type of analysis is based on the moving reference system which moves with the free stream. With this type analysis, the form of the equations looks simpler to handle. Let us write Eq. $2.24$ in the moving coordinate system which moves with the free stream. Let $x, y, z$ be the body fixed coordinate system and, $x, y, z$ be the flow fixed coordinate system. As seen from Fig. 2.3, since the free stream velocity is $U$, after the time interval $t$ the flow fixed coordinate system translates in $x$ direction by an amount $U t$.
The relation between the two coordinate system reads as
$$x^{\prime}=x-U t, \quad y^{\prime}=y, \quad z^{\prime}=z, \quad t^{\prime}=t .$$
The derivative with respect to $t^{\prime}$ becomes
$$\frac{\partial}{\partial t^{\prime}}=\frac{\partial}{\partial t}+\frac{\partial}{\partial x^{\prime}} \frac{\partial x^{\prime}}{\partial t}=\frac{\partial}{\partial t}+\frac{\partial}{\partial x^{\prime}}(-U)$$
Here, $\frac{\partial x^{\prime}}{\partial t}=-U$.
The partial derivatives with respect to body fixed coordinates in terms of the flow fixed coordinates then become:
$$\frac{\partial}{\partial t}+U \frac{\partial}{\partial x}=\frac{\partial}{\partial t^{\prime}} \quad \frac{\partial}{\partial x}=\frac{\partial}{\partial x^{\prime}} \quad \frac{\partial}{\partial y}=\frac{\partial}{\partial y^{\prime}} \quad \frac{\partial}{\partial z}=\frac{\partial}{\partial z^{\prime}}$$

# 空气动力学代考

## 物理代写|空气动力学代写空气动力学代考|加速度势

.

$$\frac{D \mathbf{q}}{\mathrm{D} t}=\nabla \psi \text {. }$$

$$\nabla \psi+\nabla \int \frac{d p}{\rho}=0$$

$$\psi=-\int \frac{d p}{\rho}+\mathrm{F}(t)$$

$$\psi=\frac{p_{\infty}-p}{\rho}$$由于压力和加速度势之间的直接关系，这个势也被称为压力积分。让我们把开尔文方程写成梯度形式
$$\nabla\left[\frac{\partial \phi}{\partial t}+\frac{q^2}{2}+\int \frac{d p}{\rho}\right]=0$$

## 物理代写|空气动力学代写空气动力学代考|移动坐标系

$$x^{\prime}=x-U t, \quad y^{\prime}=y, \quad z^{\prime}=z, \quad t^{\prime}=t .$$

$$\frac{\partial}{\partial t^{\prime}}=\frac{\partial}{\partial t}+\frac{\partial}{\partial x^{\prime}} \frac{\partial x^{\prime}}{\partial t}=\frac{\partial}{\partial t}+\frac{\partial}{\partial x^{\prime}}(-U)$$

$$\frac{\partial}{\partial t}+U \frac{\partial}{\partial x}=\frac{\partial}{\partial t^{\prime}} \quad \frac{\partial}{\partial x}=\frac{\partial}{\partial x^{\prime}} \quad \frac{\partial}{\partial y}=\frac{\partial}{\partial y^{\prime}} \quad \frac{\partial}{\partial z}=\frac{\partial}{\partial z^{\prime}}$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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