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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|电磁学代写electromagnetism代考|Conducting and Insulating Media

For a medium that is also a conductor, we have to describe the property of the medium in terms of conductivity. This leads to expression of the current density $\boldsymbol{J}$ as a function of the electric field $\boldsymbol{E}$
$$\boldsymbol{J}=\boldsymbol{J}(\boldsymbol{E})$$
Assuming that the medium is linear, the current density $\boldsymbol{J}$ and the electric field $\boldsymbol{E}$ are governed by Ohm’s law
$$\boldsymbol{J}=\sigma_{\boldsymbol{E}}+\sigma_d \star \boldsymbol{E},$$
where $\sigma$ is a $3 \times 3$ tensor real-valued function of the space variable $x$, which is called the tensor of conductivity. The quantity $\sigma_d$ is also a $3 \times 3$ tensor real-valued function, but of the time variable $t$. The convolution product is similar to (1.14): it is realized in time, enforcing the causality principle. Similarly to the constitutive relations, we shall usually restrict our studies to a perfect medium. In this case, Ohm’s law is expressed as
$$\boldsymbol{J}(t, \boldsymbol{x})=\sigma \boldsymbol{E}(t, \boldsymbol{x}) .$$
If, in addition, the medium is inhomogeneous, $\sigma=\sigma \mathbb{I}3$ and $\sigma$ is called the conductivity. In the particular case of a homogeneous medium, the conductivity is independent of $\boldsymbol{x}$. Alternatively, one could introduce the resistivity $\sigma^{-1}$ of the medium, together with the notion of a resistive medium. In most cases, the current density can be divided into two parts, $$\boldsymbol{J}=\boldsymbol{J}{e x t}+\boldsymbol{J}\sigma,$$ where $\boldsymbol{J}{\text {ext }}$ denotes an externally imposed current density, and $\boldsymbol{J}\sigma$ is the current density related to the conductivity $\pi$ of the medium by the relation (1.39). As a consequence, one has to modify Ampère’s law (1.6), which can be read as $$\Subset \frac{\partial \boldsymbol{E}}{\partial t}+\sigma \boldsymbol{E}-\operatorname{curl} \boldsymbol{H}=-\boldsymbol{J}{\text {ext }}$$

## 物理代写|电磁学代写electromagnetism代考|Time-Harmonic Maxwell Equations

We deal with time-periodic, or time-harmonic, solutions to Maxwell’s equations in a perfect medium (here, $\left.\mathbb{R}^3\right)$, with a known time dependence $\exp (-l \omega t), \omega \in$ $\mathbb{R}$. Basically, it is assumed that the time Fourier Transform of the complex-valued fields, for instance,
$$\hat{\boldsymbol{E}}\left(\omega^{\prime}, \boldsymbol{x}\right)=(2 \pi)^{-1} \int_{s \in \mathbb{R}} \boldsymbol{E}^c(s, \boldsymbol{x}) \exp \left(t \omega^{\prime} s\right) d s,$$
is of the form $\hat{\boldsymbol{E}}\left(\omega^{\prime}, \boldsymbol{x}\right)=\delta\left(\omega^{\prime}-\omega\right) \otimes \boldsymbol{e}(\boldsymbol{x})$, so that taking the reverse time Fourier Transform yields
$$\boldsymbol{E}^c(t, \boldsymbol{x})=\int_{\eta \in \mathbb{R}} \hat{\boldsymbol{E}}(\eta, \boldsymbol{x}) \exp (-\imath \eta t) d \eta=\boldsymbol{e}(\boldsymbol{x}) \exp (-\imath \omega t)$$

The real-valued (physical) solutions are then written as
\begin{aligned} &\boldsymbol{E}(t, \boldsymbol{x})=\Re(\boldsymbol{e}(\boldsymbol{x}) \exp (-t \omega t)) \ &\boldsymbol{H}(t, \boldsymbol{x})=\Re(\boldsymbol{h}(\boldsymbol{x}) \exp (-t \omega t)) \ &\boldsymbol{D}(t, \boldsymbol{x})=\Re(\boldsymbol{d}(\boldsymbol{x}) \exp (-t \omega t)) \ &\boldsymbol{B}(t, \boldsymbol{x})=\Re(\boldsymbol{b}(\boldsymbol{x}) \exp (-t \omega t)) \end{aligned}
Equivalently, one has $\left.\boldsymbol{E}(t, \boldsymbol{x})=\frac{1}{2}{\boldsymbol{e}(\boldsymbol{x}) \exp (-t \omega t)+\overline{\boldsymbol{e}}(\boldsymbol{x}) \exp (t \omega t))\right}$, etc. As a consequence, one can restrict the study of time-harmonic fields to positive values of $\omega$, which is called the pulsation. It is related to the frequency $v$ by the formula $\omega=2 \pi v$

Remark 1.2.1 Formally, for a pulsation $\omega$ equal to zero, one gets static fields, in the sense that they are independent of time. In this way, static fields are a “special instance” among stationary fields.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Conducting and Insulating Media

$$\boldsymbol{J}=\boldsymbol{J}(\boldsymbol{E})$$

$$\boldsymbol{J}=\sigma_{\boldsymbol{E}}+\sigma_d \star \boldsymbol{E},$$

$$\boldsymbol{J}(t, \boldsymbol{x})=\sigma \boldsymbol{E}(t, \boldsymbol{x}) .$$

$$\boldsymbol{J}=\boldsymbol{J} e x t+\boldsymbol{J} \sigma,$$

$$\Subset \frac{\partial \boldsymbol{E}}{\partial t}+\sigma \boldsymbol{E}-\operatorname{curl} \boldsymbol{H}=-\boldsymbol{J} \text { ext }$$

## 物理代写|电磁学代写electromagnetism代考|Time-Harmonic Maxwell Equations

$$\hat{\boldsymbol{E}}\left(\omega^{\prime}, \boldsymbol{x}\right)=(2 \pi)^{-1} \int_{s \in \mathbb{R}} \boldsymbol{E}^c(s, \boldsymbol{x}) \exp \left(t \omega^{\prime} s\right) d s$$

$$\boldsymbol{E}^c(t, \boldsymbol{x})=\int_{\eta \in \mathbb{R}} \hat{\boldsymbol{E}}(\eta, \boldsymbol{x}) \exp (-\imath \eta t) d \eta=\boldsymbol{e}(\boldsymbol{x}) \exp (-\imath \omega t)$$

$$\boldsymbol{E}(t, \boldsymbol{x})=\Re(\boldsymbol{e}(\boldsymbol{x}) \exp (-t \omega t)) \quad \boldsymbol{H}(t, \boldsymbol{x})=\Re(\boldsymbol{h}(\boldsymbol{x}) \exp (-t \omega t)) \boldsymbol{D}(t, \boldsymbol{x})=\Re(\boldsymbol{d}(\boldsymbol{x}) \exp (-t \omega t)) \quad \boldsymbol{B}(t, \boldsymbol{x})=\Re(\boldsymbol{b}(\boldsymbol{x}) \exp (-t \omega t))$$

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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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师