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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|电动力学代写electromagnetism代考|MATHEMATICAL ApProach

As we have previously seen, we can only apply Coulomb’s law, and hence use our usual expressions for $\boldsymbol{D}$ and $\boldsymbol{E}$, when considering point charges. However, we have a surface charge, and so how can we analyze this situation? The solution is to consider a small section of the disc, calculate the flux density due to the charge on this small section and integrate the result over the area of the disc. (Problem $1.2$ gives more information about the integration method used in the following derivation.)

As Figure $2.15$ shows, let us consider a small section of a disc. The area of this small section is
$$\mathrm{d} s=r \mathrm{~d} \phi \mathrm{d} r$$ if $\mathrm{d} \phi$ is expressed in radians. (This is a direct consequence of expressing $\mathrm{d} \phi$ in radians. The circumference of the disc is $2 \pi r$, and this encloses an angle of $360^{\circ}$, or $2 \pi$ radians. So, the length of an arc that subtends an angle of $180^{\circ}$, or $\pi$ radians, is $\pi r$. Thus, the length of an arc is equal to the product of the angle (in radians) and the radius of the arc.)
If we have a charge spread over the surface of this disc, the charge on this small section is
$$\mathrm{d} Q=p_s \mathrm{~d} s$$
which we can take to be a point charge if $\mathrm{d} s$ is very small. This charge will produce a small component of the flux density acting in the direction shown in Figure 2.15a. So,
$$\mathrm{d} \boldsymbol{D}=\frac{p_s \mathrm{~d} s}{4 \pi l^2}$$
We can resolve this flux density into horizontal and vertical components, and then integrate with respect to $\Phi$ between the limits 0 and $2 \pi$. This integration will describe a ring of thickness $\mathrm{d} r$ and radius $r$. It is then a matter of integrating with respect to $r$ to map out the whole of the disc. However, when we integrate with respect to $\Phi$, we find that the horizontal component of $\boldsymbol{D}$ will be zero. This is a consequence of the symmetry of the disc, similar to the symmetry we met in the previous section. (Readers can check this by performing the integration for themselves.)

## 物理代写|电动力学代写electromagnetism代考|VOLUME CHARGES

The previous two sections have introduced us to line and surface charge densities. However, we live in a three-dimensional world (four if you count time) and so we will often meet charged volumes. When considering a volume charge density, we can make good use of Gauss’ law to replace the volume charge by a point charge at the centre of the volume.

As an example, let us consider a sphere with a charge evenly distributed throughout its volume, as shown in Figure 2.16a. To analyze this situation, we could consider a small section of the sphere, and perform an integration to map out the whole of the volume. However, this will involve us in a considerable amount of work. An alternative is to apply Gauss’ law and replace the volume charge density by a point charge at the centre of the volume.

So, if the sphere has a total charge of coulomb distributed throughout the volume, we can replace the sphere by a point charge, placed at the centre placed the centre of the sphere, of magnitude $Q$. This is shown in Figure 2.16b. It is then a simple to find the flux density, etc., at any distance from the surface of the sphere.

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|MATHEMATICAL ApProach

$$\mathrm{d} s=r \mathrm{~d} \phi \mathrm{d} r$$

$$\mathrm{d} Q=p_s \mathrm{~d} s$$

$$\mathrm{d} \boldsymbol{D}=\frac{p_s \mathrm{~d} s}{4 \pi l^2}$$

## 有限元方法代写

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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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