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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|Bibliographical Notes

Concerning the form of Maxwell’s equations, we relied on the physical approach of Jackson [141, Chapter 1] and on the topological approach of Gross and Kotiuga [127]. See also the book by Jones [148]. As far as the constitutive relations are concerned, References $[141,149,152,156]$ have been helpful. The experimental results acquiréd a historical status a long time ago, cf. Coulomb’s experiments in 1785. The “existence” results of electromagnetic fields in all space $\mathbb{R}^3$ can be found in many places: we chose $[140]$ for the general case of a chiral medium and Chapter 6 in the monograph by Cessenat [72] for the particular case of a homogeneous medium. In regard to conducting media, we used the numerical results from [127, Chapter 1]. Regarding the issue of vanishing electromagnetic fields inside perfect conductors, we mention [167, Chapter 5], where illuminating comments and (partial) mathematical justification can be found. Let us mention $[94,141,142,161,195]$ for the definition of skin depth in different models ; see also [191] for the notion of magnetic skin depth.

On the vast topic of the stationary Maxwell equations, we refer the reader (for instance) to the introductory book by Laval [153]. and to the monograph by Krall and Trivelpiece [151]. See also the book by Van Bladel [201]. The limiting amplitude principle is rigorously proven in the monograph by Sanchez and Sanchez [183].

As far as the approximate models are concerned, we refer the reader to the works of Raviart and co-workers $[96,176]$, where the general methodology on how to build those models is described. In geophysics, approximate models are considered, for instance, in $[41,85]$. The static models have been scrutinized extensively by Durand in his three-volume series [103]: in particular, an impressive number of computations carried out by hand (before the era of personal computers) are available. The Darwin model is named after C. G. Darwin, who studied the motion of charged particles in the 1920s [90]. In bounded domains, References [83, 96] provide some insight as to how one can define suitable boundary conditions for the transverse and longitudinal parts of the electric field.

## 物理代写|电磁学代写electromagnetism代考|Function Spaces for Scalar Fields

Unless otherwise specified, the function spaces will be defined on a subset of $\mathbb{R}^n$ (possibly $\mathbb{R}^n$ itself). The definitions and properties that we list hereafter can depend on the category of subsets of $\mathbb{R}^n$ on which they are given. We shall consider three categories: (C1) open subsets, (C2) open subsets with Lipschitz boundary, and (C3) bounded, open connected subsets with Lipschitz boundary, also called domains. The last category will include an important subcategory, the curved polyhedra, that is, domains with a piecewise smooth, curved boundary.

An element $\alpha=\left(\alpha_1, \cdots, \alpha_n\right)$ of $\mathbb{N}^n$ is called a multi-index, with $|\alpha|=$ $\sum_{j=1}^n \alpha_j$. The partial derivative of order $\alpha$ is further denoted by
$$\partial_\alpha f=\frac{\partial^{|\alpha|} f}{\partial x_1^{\alpha_1} \cdots \partial x_n^{\alpha_n}}$$
Let $d \boldsymbol{x}=d x_1 d x_2 \cdots d x_n$ denote the Lebesgue measure in $\mathbb{R}^n$.

Category $(C 1)$ Open subsets of $\mathbb{R}^n$.
Consider a set $\Omega$ that belongs to the category (C1).
Let us begin with the Lebesgue spaces $L^p(\Omega)$, for $1 \leq p \leq \infty$. One usually considers complex-valued functions, hut all definitions are easily extended to realvalued function spaces. Details on Banach and Hilbert spaces, and also on the duality and interpolation theories, can be found in Sect. 4.1.

Definition 2.1.1 The space $L^p(\Omega)$ is composed of all complex-valued, Lebesguemeasurable functions $f$ on $\Omega$, and such that
$$\left{\begin{array}{l} \text { for } 1 \leq p<\infty|f|_{L^p(\Omega)}:=\left{\int_{\Omega}|f|^p d x\right}^{1 / p}<\infty \ \text { for } p=\infty \quad|f|_{L^{\infty}(\Omega)}:=\operatorname{esssup}{x \in \Omega}|f(x)|<\infty \end{array} .\right.$$ Endowed with the norm $|\cdot|{L^p(\Omega)}, L^p(\Omega)$ is a Banach space and, for $1 \leq p<\infty$, is separable.

Let $p \in[1, \infty], f_1=f_2$ in $L^p(\Omega)$ mean that $f_1, f_2 \in L^p(\Omega)$ and $f_1=f_2$ almost everywhere in $\Omega$. One can then define the spaces of functions that are locally in $L^p$ in the following way. If ${ }^1 f \mathbf{1}K$ belongs to $L^p(\Omega)$ for every compact subset $K$ of $\Omega$, then $f$ is locally in $L^p(\Omega)$, and one writes $$f \in L{l o c}^p(\Omega) .$$
One then has a stability result of the multiplication by elements of $L^{\infty}(\Omega)$.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Function Spaces for Scalar Fields

∂一个F=∂|一个|F∂X1一个1⋯∂Xn一个n

$$\left{\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别。\正确的。$$ 赋有规范|⋅|大号p(哦),大号p(哦)是 Banach 空间，对于1≤p<∞, 是可分离的。

## 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。

assignmentutor™您的专属作业导师
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