物理代写|电磁学代写electromagnetism代考|PHYS3040

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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|Physical Framework and Models

The aim of this first chapter is to present the physics framework of electromagnetism, in relation to the main sets of equations, that is, Maxwell’s equations and some related approximations. In that sense, it is neither a purely physical nor a purely mathematical point of view. The term model might be more appropriate: sometimes, it will be necessary to refer to specific applications in order to clarify our purpose, presented in a selective and biased way, as it leans on the authors’ personal view. This being stated, this chapter remains a fairly general introduction, including the foremost models in electromagnetics. Although the choice of such applications is guided by our own experience, the presentation follows a natural structure.
Consequently, in the first section, we introduce the electromagnetic fields and the set of equations that governs them, namely Maxwell’s equations. Among others, we present their integral and differential forms. Next, we define a class of constitutive relations, which provide additional relations between electromagnetic fields and are needed to close Maxwell’s equations. Then, we briefly review the solvability of Maxwell’s equations, that is, the existence of electromagnetic fields, in the presence of source terms. We then investigate how they can be reformulated as potential problems. Finally, we relate some notions on conducting media.

In Sect. 1.2, we address the special case of stationary equations, which have timeperiodic solutions, the so-called time-harmonic fields. The useful notion of plane waves is also introduced, as a particular case of the time-harmonic solutions.

Maxwell’s equations are related to electrically charged particles. Hence, there exists a strong correlation between Maxwell’s equations and models that describe the motion of particles. This correlation is at the core of most models in which Maxwell’s equations are coupled with other sets of equations: two of them-the Vlasov-Maxwell model and an example of a magnetohydrodynamics model (or MHD)—will be detailed in Sect. 1.3.

物理代写|电磁学代写electromagnetism代考|Integral Maxwell Equations

The propagation of the electromagnetic fields in continuum media is described using four space- and time-dependent functions. If we respectively denote by $\boldsymbol{x}=\left(x_1, x_2, x_3\right)$ and $t$ the space and time variables, these four $\mathbb{R}^3$-valued, or vectorvalued, functions defined in time-space $\mathbb{R} \times \mathbb{R}^3$ are

1. the electric field $\boldsymbol{E}$,
2. the magnetic induction $\boldsymbol{B}$,
3. the magnetic field ${ }^2 \boldsymbol{H}$,
4. the electric displacement $\boldsymbol{D}$.
These vector functions are governed by the integral Maxwell equations below. These four equations are respectively called Ampère’s law, Faraday’s law, Gauss’s law and the absence of magnetic monopoles. They read as (system of units SI)
\begin{aligned} \frac{d}{d t}\left(\int_S \boldsymbol{D} \cdot \boldsymbol{d} \boldsymbol{S}\right)-\int_{\partial S} \boldsymbol{H} \cdot d \boldsymbol{l} &=-\int_S \boldsymbol{J} \cdot \boldsymbol{d} \boldsymbol{S} \ \frac{d}{d t}\left(\int_{S^{\prime}} \boldsymbol{B} \cdot \boldsymbol{d} \boldsymbol{S}\right)+& \int_{\partial S^{\prime}} \boldsymbol{E} \cdot d \boldsymbol{l}=0 \ & \int_{\partial V} \boldsymbol{D} \cdot \boldsymbol{d} \boldsymbol{S}=\int_V \varrho d V \ \int_{\partial V^{\prime}} \boldsymbol{B} \cdot \boldsymbol{d} \boldsymbol{S} &=0 \end{aligned}
Above, $S, S^{\prime}$ are any surface of $\mathbb{R}^3$, and $V, V^{\prime}$ are any volume of $\mathbb{R}^3$. One can write elements $d S$ and $d l$ as $d S=n d S$ and $d l=\tau d l$, where $n$ and $\tau$ are, respectively, the unit outward normal vector to $S$ and the unit tangent vector to the curve $\partial S$. When $S$ is the closed surface bounding a volume, then $\boldsymbol{n}$ is pointing outward from the enclosed volume. Similarly, the unit tangent vector to $\partial S$ is pointing in the direction given by the right-hand rule.

物理代写|电磁学代写electromagnetism代考|Integral Maxwell Equations

1. 电场 $\boldsymbol{E}$,
2. 磁感应 $\boldsymbol{B}$,
3. 磁场 ${ }^2 \boldsymbol{H}$,
4. 电位移 $\boldsymbol{D}$.
这些向量函数由下面的积分麦克斯韦方程控制。这四个方程分别称为安培定律、法拉第定律、高斯定律和不 存在磁单极子。它们读作（单位制 SI)
$$\frac{d}{d t}\left(\int_S \boldsymbol{D} \cdot \boldsymbol{d} \boldsymbol{S}\right)-\int_{\partial S} \boldsymbol{H} \cdot d \boldsymbol{l}=-\int_S \boldsymbol{J} \cdot \boldsymbol{d} \boldsymbol{S} \frac{d}{d t}\left(\int_{S^{\prime}} \boldsymbol{B} \cdot \boldsymbol{d} \boldsymbol{S}\right)+\int_{\partial S^{\prime}} \boldsymbol{E} \cdot d \boldsymbol{l}=0 \int_{\partial V} \boldsymbol{D}$$
以上，S, $S^{\prime}$ 是任何表面 $\mathbb{R}^3$ ，和 $V, V^{\prime}$ 是任何体积 $\mathbb{R}^3$. 一个可以写元素 $d S$ 和 $d l$ 作为 $d S=n d S$ 和 $d l=\tau d l$ ，在哪里 $n$ 和 $\tau$ 分别是单位外向法向量 $S$ 和曲线的单位切向量 $\partial S$. 什么时候 $S$ 是包围一个体积的封闭曲面，那 么 $\boldsymbol{n}$ 从封闭的体积向外指向。类似地，单位切向量为 $\partial S$ 指向右手定则给出的方向。

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。