## 物理代写|量子光学代写Quantum Optics代考|PHYS686

statistics-lab™ 为您的留学生涯保驾护航 在代写量子光学Quantum Optics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子光学Quantum Optics代写方面经验极为丰富，各种代写量子光学Quantum Optics相关的作业也就用不着说。

• 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|量子光学代写Quantum Optics代考|The Nabla Operator

Gradient. Consider a scalar function $f(x, y, z)$ that depends on all three spatial coordinates. The total derivative of $f$ becomes
$$d f=\frac{\partial f}{\partial x} d x+\frac{\partial f}{\partial y} d y+\frac{\partial f}{\partial z} d z=\nabla f \cdot d \ell$$
We have introduced the infinitesimal position change
$$d \ell=\hat{\boldsymbol{x}} d x+\hat{\boldsymbol{y}} d y+\hat{z} d z,$$
and the nabla operator
$$\nabla=\hat{x} \frac{\partial}{\partial x}+\hat{y} \frac{\partial}{\partial y}+\hat{z} \frac{\partial}{\partial z}$$
To be meaningful, $\nabla$ must act on some function such as $f(\boldsymbol{r})$ in Eq. (2.6). If we rewrite Eq. (2.6) in the form
$$d f-|\nabla f||d \ell| \cos \theta$$
where $\theta$ is the angle between $\nabla f$ and $d \ell$, we observe that $d f$ becomes largest when both vectors are parallel, this is for $\theta=0$. In other words, if we move in the same direction as $\nabla f$ the total change $d f$ is maximized. Thus $\nabla f$, which is usually called the “gradient” of $f$, points into the direction where $f(\boldsymbol{r})$ changes most.

## 物理代写|量子光学代写Quantum Optics代考|Gauss’ and Stokes’ Theorem

We will often employ two integral theorems. The first one is Gauss’ theorem
$$\int_{\Omega} \nabla \cdot \boldsymbol{F}(\boldsymbol{r}) d^3 r=\oint_{\partial \Omega} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{S},$$
which states that the integral of $\nabla \cdot \boldsymbol{F}$ over a volume $\Omega$ equals the (directed) flow of the vector field through the boundary $\partial \Omega$ of the volume. Here $d S=\hat{n} d S$, where $\hat{n}$ is the outer surface normal and $d \boldsymbol{S}$ denotes an infinitesimal surface element. Figure 2.4a gives a graphical interpretation of this theorem in terms of the previously introduced plaquettes. As the divergence measures the net difference between inand out-flow in a given square element, the in and out fluxes $\Rightarrow \Leftrightarrow$ of two neighbor elements precisely cancel each other, and the only non-vanishing contributions are located at the boundary.
The second theorem is Stokes’ theorem
$$\int_S \nabla \times \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{S}=\oint_{\partial S} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{\ell},$$
which states that the integration of the curl of a vector function over an open surface $S$ equals the line integral of $\boldsymbol{F}(\boldsymbol{r})$ along the boundary $\partial S$ of the surface. Figure $2.4 \mathrm{~b}$ gives a graphical interpretation of this theorem in terms of the previously introduced plaquettes. The curl contributions cancel each other at the edges of neighbor elements, such as $\langle\Omega$, and the only non-vanishing contributions are located at the surface boundary.

In which direction does the outer surface normal of $d \boldsymbol{S}=\hat{\boldsymbol{n}} d S$ point? And in which direction goes $d \ell$ ? In case of Gauss’ theorem $\hat{\boldsymbol{n}}$ points to the outside of the volume. If one wants to define the boundary differently, and we will do so in later parts of the book, one has to be careful about this point. Similarly, the direction of $d S$ dictates the circulation of $d \ell$ according to the right-hand rule, which means that if one points with the thumb of the right hand upwards (pointing in the direction of $\hat{\boldsymbol{n}}$ ) the other fingers point in the direction of $d \ell$.

## 物理代写|量子光学代写Quantum Optics代考|纳布拉操作员

$$d f=\frac{\partial f}{\partial x} d x+\frac{\partial f}{\partial y} d y+\frac{\partial f}{\partial z} d z=\nabla f \cdot d \ell$$

$$d \ell=\hat{\boldsymbol{x}} d x+\hat{\boldsymbol{y}} d y+\hat{z} d z,$$

$$\nabla=\hat{x} \frac{\partial}{\partial x}+\hat{y} \frac{\partial}{\partial y}+\hat{z} \frac{\partial}{\partial z}$$
，为了有意义，$\nabla$必须作用于某些函数，如式(2.6)中的$f(\boldsymbol{r})$。如果我们将式(2.6)改写为
$$d f-|\nabla f||d \ell| \cos \theta$$
，其中$\theta$是$\nabla f$和$d \ell$之间的夹角，我们观察到当两个向量平行时$d f$最大，这是对于$\theta=0$。换句话说，如果我们向$\nabla f$的同一个方向移动，那么$d f$的总变化是最大的。因此，$\nabla f$通常被称为$f$的“梯度”，它指向$f(\boldsymbol{r})$变化最大的方向

## 物理代写|量子光学代写量子光学代考|高斯和斯托克斯定理

$$\int_{\Omega} \nabla \cdot \boldsymbol{F}(\boldsymbol{r}) d^3 r=\oint_{\partial \Omega} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{S},$$
，它表明$\nabla \cdot \boldsymbol{F}$对体积$\Omega$的积分等于向量场通过体积边界$\partial \Omega$的(有向)流。这里是$d S=\hat{n} d S$，其中$\hat{n}$是外表面法线，$d \boldsymbol{S}$表示一个无穷小的表面元素。图2.4a给出了根据前面介绍的斑块对该定理的图解解释。由于散度度量的是给定正方形元素流入和流出之间的净差，两个相邻元素的流入和流出通量$\Rightarrow \Leftrightarrow$恰好相互抵消，唯一不消失的贡献位于边界。第二个定理是Stokes定理
$$\int_S \nabla \times \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{S}=\oint_{\partial S} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{\ell},$$
，该定理指出向量函数的旋度在开放曲面$S$上的积分等于$\boldsymbol{F}(\boldsymbol{r})$沿曲面边界$\partial S$的线积分。图$2.4 \mathrm{~b}$给出了根据前面介绍的斑块对该定理的图形解释。旋度贡献在相邻元素的边缘相互抵消，例如$\langle\Omega$，唯一不消失的贡献位于曲面边界 $d \boldsymbol{S}=\hat{\boldsymbol{n}} d S$的外表面法线指向哪个方向?$d \ell$的方向是什么?在高斯定理的情况下$\hat{\boldsymbol{n}}$指向体积的外面。如果有人想用不同的方式定义边界，我们将在本书后面的部分中这么做，那么在这一点上必须小心。同样，根据右手规则，$d S$的方向决定了$d \ell$的循环，这意味着如果一个人用右手的拇指指向上面(指向$\hat{\boldsymbol{n}}$的方向)，其他手指指向$d \ell$的方向。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子光学代写Quantum Optics代考|OSE6347

statistics-lab™ 为您的留学生涯保驾护航 在代写量子光学Quantum Optics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子光学Quantum Optics代写方面经验极为丰富，各种代写量子光学Quantum Optics相关的作业也就用不着说。

• 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|量子光学代写Quantum Optics代考|The Realm of Nano Optics

Figure $1.7$ shows the wavelengths (bottom axis) and photon energies (top axis) for the near-infrared, visible, and ultraviolet part of the electromagnetic spectrum. The visible regime ranges from $380-750 \mathrm{~nm}$, and correspondingly the diffraction limit is in the micrometer rather than nanometer regime. Thus, optics and nanoscience do not come naturally together! Nano optics is the science that tries to push optics to the nanoscale despite these limitations.

First, and most importantly, we have to realize that the diffraction limit is based on fundamental laws of physics, most importantly the dispersion relation which is deeply rooted in the fundamental wave equation. From the dispersion relation we find that there exist two types of waves, propagating and evanescent ones, and the decay of the latter waves is responsible for the loss of resolution. Using conventional optics it is not possible to resolve objects that are closer to each other than the wavelength of light $\lambda$, and conversely we cannot focus light to spots that are smaller in dimension than $\lambda$. In order to overcome the diffraction limit of light we can hardly compete with the fundamental laws of physics, thus we have to change the rules of the game. Nano optics has come up with a number of successful solutions, which will be discussed in detail in this book. Figure $1.8$ shows three representative examples.

Nearfield Optics. In scanning nearfield optical microscopy (SNOM) an optical fiber is brought into close vicinity of a nano object, see panel (a). Through the fiber tip, the evanescent nearfields of the nano object can be converted into propagating photons, which are detected at the other end of the fiber. By raster-scanning the fiber over the specimen, one obtains information about the optical nearfields with nanometer resolution.

## 物理代写|量子光学代写Quantum Optics代考|The Concept of Fields

Electrostatics can be briefly summarized through Coulomb’s law that describes how a particle with charge $q_1$ situated at position $\boldsymbol{r}1$ becomes attracted or repelled by a second particle with charge $q_2$ situated at position $\boldsymbol{r}_2$, $$\boldsymbol{F}{12}=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{\boldsymbol{r}}{12}$$ Here $\varepsilon_0$ is the vacuum permittivity, which appears because of the SI unit system under use, $r{12}=\boldsymbol{r}1-\boldsymbol{r}_2$ is the distance vector between the two charges, and $\hat{\boldsymbol{r}}{12}$ is the unit vector pointing in the direction of $\boldsymbol{r}_{12}$. Let me emphasize a few important points about Coulomb’s law of Eq. (2.1).

Symmetry. Coulomb’s law only depends on the relative distance vector $\boldsymbol{r}_{12}$. For this reason, it respects the homogeneity of space (no point of space is distinguished with respect to any other one) and the isotropy of space (no direction in space is distinguished with respect to another one). We will come back to this point in Chap. 4 when discussing the symmetries of the electromagnetic fields.

We also note in passing that the $1 / r^2$ dependence of Coulomb’s law is the only distance dependence compatible with massless photons as force carriers of the field [2].
Superposition. When two or more charged particles are present, the total force can be simply computed by adding the respective forces together,
$$\boldsymbol{F}1=\boldsymbol{F}{12}+\boldsymbol{F}{13}+\cdots+\boldsymbol{F}{1 n}=\frac{1}{4 \pi \varepsilon_0} \sum_{j=2}^n \frac{q_1 q_j}{r_{1 j}^2} \hat{\boldsymbol{r}}_{1 j} .$$
This is the essence of the so-called superposition principle that has been tested experimentally to the highest degree of precision [2], and which plays an important role in the theory of electromagnetism.
Charge Distribution. In many situations we do not want to deal with pointlike particles but with a continuous charge distribution $\rho(\boldsymbol{r})$. Suppose that many particles are present within a small volume element $\Delta V_i$ and we are only interested in the fields on sufficiently larger length scales. We may then group together the particles in small bunches $\Delta q_i$ and relate them to the charge distribution $\rho(\boldsymbol{r})$ via
$$\Delta q_i \approx \rho\left(\boldsymbol{r}_i\right) \Delta V_i$$
Although the limit $\Delta V \rightarrow 0$ is not meaningful for point-like particles, we can still introduce a continuous charge distribution $\rho(\boldsymbol{r})$, which is expected to vary smoothly as a function of $\boldsymbol{r}$ (see Chap.

## 物理代写|量子光学代写量子光学代考|场的概念

$$\Delta q_i \approx \rho\left(\boldsymbol{r}_i\right) \Delta V_i$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子光学代写Quantum Optics代考|PHYS248

statistics-lab™ 为您的留学生涯保驾护航 在代写量子光学Quantum Optics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子光学Quantum Optics代写方面经验极为丰富，各种代写量子光学Quantum Optics相关的作业也就用不着说。

• 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|量子光学代写Quantum Optics代考|One-Dimensional Waves

What are waves? I encourage the reader to reflect a while about this question and to come up with a meaningful answer. After all, waves are abundant in physics, ranging from water and sound waves to electromagnetic ones, which are the central objects of this book. However, it seems rather difficult to explain what a wave really is. In the book “Introduction to Electrodynamics” Griffiths comes up with the following definition [1]:

A wave is a disturbance of a continuous medium that propagates with a fixed shape at a constant velocity.

This definition leaves a number of open questions (what is the continuous medium in case of electromagnetic waves? what about dispersive media?), and I will propose later a modified, albeit more technical definition. To get started, let us take Griffiths’ description and consider waves in one spatial dimension. We denote the wave disturbance propagating along $x$ with $f(x, t)$, where $t$ is the time. Figure 1 .1 shows a schematic sketch of such a wave propagation. After a time $t$ the initial wave has been displaced by a distance $v t$. We can thus write
$$f(x, 0)=g(x), \quad f(x, t)=g(x-v t),$$
which shows that $f$ is a function of one combined variable $u=x-v t$ rather than of two independent variables $x, t$. The same analysis applies to a wave that moves to the left, and the general solution is a superposition of left- and right-moving waves
$$f(x, t)=g_{-}(x-v t)+g_{+}(x+v t)=g_{-}\left(u_{-}\right)+g_{+}\left(u_{+}\right), \quad u_{\pm}=x \pm v t .$$
It is now easy to show that
$$\left(\frac{\partial}{\partial x}+\frac{1}{v} \frac{\partial}{\partial t}\right) g_{-}\left(u_{-}\right)=\left(\frac{\partial u_{-}}{\partial x}+\frac{1}{v} \frac{\partial u_{-}}{\partial t}\right) \frac{d g\left(u_{-}\right)}{d u_{-}}=\left(1-\frac{v}{v}\right) \frac{d g\left(u_{-}\right)}{d u_{-}}=0 .$$
Thus, the operator on the left-hand side equates all right-moving waves to zero. Similarly, we find for the left-moving waves
$$\left(\frac{\partial}{\partial x}-\frac{1}{v} \frac{\partial}{\partial t}\right) g_{+}\left(u_{+}\right)=\left(\frac{\partial u_{-}}{\partial x}-\frac{1}{v} \frac{\partial u_{+}}{\partial t}\right) \frac{d g\left(u_{+}\right)}{d u_{+}}=\left(1-\frac{v}{v}\right) \frac{d g\left(u_{+}\right)}{d u_{+}}=0 .$$
If we apply both operators on the wavefunction $f(x, t)$, we equate the left- and right-moving waves to zero, and we arrive at the scalar wave equation in one spatial dimension.

## 物理代写|量子光学代写Quantum Optics代考|Three-Dimensional Waves

So how do things change when we go from one to three spatial dimensions? Formally not that much. Instead of Eq. (1.1) we get
Scalar Wave Equation for Three Spatial Dimensions
$$\left(\nabla^2-\frac{1}{v^2} \frac{\partial^2}{\partial t^2}\right) f(\boldsymbol{r}, t)=0,$$
where $f(\boldsymbol{r}, t)$ is the scalar wavefunction depending on $\boldsymbol{r}=(x, y, z)$, and $\nabla^2$ is the usual Laplace operator
$$\nabla^2-\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2} .$$
Similarly to the decomposition into sinusoidal waves of Eq. (1.4) we introduce plane waves
Plane Wave in Three Spatial Dimensions
$$f(x, t)=A e^{i(\boldsymbol{k} \cdot \boldsymbol{r}-\omega t)},$$
where $A$ is the amplitude and $\boldsymbol{k}=k \hat{\boldsymbol{n}}$ is the wavevector that has the length $k=2 \pi / \lambda$ determined by the wavelength $\lambda$ and points in the direction of the wave propagation, see Fig. 1.2. With these plane waves we can define in complete analogy to Eq. (1.6) the three-dimensional Fourier transform
$$\begin{gathered} f(\boldsymbol{r})-\int_{-\infty}^{\infty} e^{+i k \cdot \boldsymbol{r}} \tilde{f}(\boldsymbol{k}) \frac{d^3 k}{(2 \pi)^3} \ \tilde{f}(\boldsymbol{k})=\int_{-\infty}^{\infty} e^{-i \boldsymbol{k} \cdot \boldsymbol{r}} f(\boldsymbol{r}) d^3 r \end{gathered}$$

## 物理代写|量子光学代写Quantum Optics代考|一维波

$$f(x, 0)=g(x), \quad f(x, t)=g(x-v t),$$
，这表明$f$是一个组合变量$u=x-v t$的函数，而不是两个自变量$x, t$的函数。同样的分析也适用于向左移动的波，其通解是向左移动波和向右移动波的叠加
$$f(x, t)=g_{-}(x-v t)+g_{+}(x+v t)=g_{-}\left(u_{-}\right)+g_{+}\left(u_{+}\right), \quad u_{\pm}=x \pm v t .$$

$$\left(\frac{\partial}{\partial x}+\frac{1}{v} \frac{\partial}{\partial t}\right) g_{-}\left(u_{-}\right)=\left(\frac{\partial u_{-}}{\partial x}+\frac{1}{v} \frac{\partial u_{-}}{\partial t}\right) \frac{d g\left(u_{-}\right)}{d u_{-}}=\left(1-\frac{v}{v}\right) \frac{d g\left(u_{-}\right)}{d u_{-}}=0 .$$

$$\left(\frac{\partial}{\partial x}-\frac{1}{v} \frac{\partial}{\partial t}\right) g_{+}\left(u_{+}\right)=\left(\frac{\partial u_{-}}{\partial x}-\frac{1}{v} \frac{\partial u_{+}}{\partial t}\right) \frac{d g\left(u_{+}\right)}{d u_{+}}=\left(1-\frac{v}{v}\right) \frac{d g\left(u_{+}\right)}{d u_{+}}=0 .$$

## 物理代写|量子光学代写Quantum Optics代考|三维波

$$\left(\nabla^2-\frac{1}{v^2} \frac{\partial^2}{\partial t^2}\right) f(\boldsymbol{r}, t)=0,$$

$$\nabla^2-\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2} .$$

$$f(x, t)=A e^{i(\boldsymbol{k} \cdot \boldsymbol{r}-\omega t)},$$
，其中$A$是振幅，$\boldsymbol{k}=k \hat{\boldsymbol{n}}$是波长$\lambda$决定长度$k=2 \pi / \lambda$并指向波传播方向的波矢，如图1.2所示。有了这些平面波，我们可以完全类似于式(1.6)定义三维傅里叶变换
$$\begin{gathered} f(\boldsymbol{r})-\int_{-\infty}^{\infty} e^{+i k \cdot \boldsymbol{r}} \tilde{f}(\boldsymbol{k}) \frac{d^3 k}{(2 \pi)^3} \ \tilde{f}(\boldsymbol{k})=\int_{-\infty}^{\infty} e^{-i \boldsymbol{k} \cdot \boldsymbol{r}} f(\boldsymbol{r}) d^3 r \end{gathered}$$

## 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。