## 物理代写|光学工程代写Optical Engineering代考|EGEE480

statistics-lab™ 为您的留学生涯保驾护航 在代写光学工程Optical Engineering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。我们的专家在代写光学工程Optical Engineering代写方面经验极为丰富，各种代写光学工程Optical Engineering相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|光学工程代写Optical Engineering代考|Interference and Diffraction

Consider two sinusoidal waves passing from point $\mathrm{A}$ to point $\mathrm{C}$ and from point $\mathrm{B}$ to point C. For simplicity, the frequencies of the two waves are the same. Vectors of AC and $\mathrm{BC}$ are denoted by $\boldsymbol{r}{A C}$ and $\boldsymbol{r}{B C}$, respectively, and their wave number vectors by $\boldsymbol{k}A$ and $\boldsymbol{k}_B$, respectively (see Fig. 2.1). The plane wave arriving at point $\mathrm{C}$ from point $A$ is given by $$u_A=A_A \exp \left[\mathbf{i}\left(\boldsymbol{k}_A \cdot \boldsymbol{r}{A C}+\phi_A-\omega t\right)\right],$$
and the plane wave arriving at point $\mathrm{C}$ from point $\mathrm{B}$ is
$$u_B=A_B \exp \left[\mathrm{i}\left(\boldsymbol{k}B \cdot \boldsymbol{r}{B C}+\phi_B-\omega t\right)\right] .$$
Suppose the position vectors of points A and C are $\boldsymbol{r}A\left(x_A, y_A, z_A\right)$ and $\boldsymbol{r}_C\left(x_C, y_C, z_C\right)$, we have $$r{A C}=r_C-r_A .$$
By using Eq. (1.30), we have
\begin{aligned} \boldsymbol{k}A \cdot \boldsymbol{r}{A C} & =\boldsymbol{k} \cdot\left(\boldsymbol{r}C-\boldsymbol{r}_A\right) \ & =\frac{2 \pi}{\lambda_0} n\left[\left(x_C-x_A\right) \cos \alpha_A+\left(y_C-y_A\right) \cos \beta_A+\left(z_C-z_A\right) \cos \gamma_A\right], \end{aligned} where the directional cosines of the vector $\boldsymbol{k}_A$ are $\left(\cos \alpha_A, \cos \beta_A, \cos \gamma_A\right)$. If $$\left(x_C-x_A\right) \cos \alpha_A+\left(y_C-y_A\right) \cos \beta_A+\left(z_C-z_A\right) \cos \gamma_A=l{A C},$$
then $l_{A C}$ gives the distance between points A and $\mathrm{C}$, and $n l_{A C}$ is called the optical distance, where $n$ is the refractive index of the medium. Equations (2.1) and (2.2) are rewritten as
$$u_A=A_A \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{A C}+\phi_A-\omega t\right)\right]$$ and
$$u_B=A_B \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{B C}+\phi_B-\omega t\right)\right],$$
respectively. Since the amplitude $u_C$ at point $\mathrm{C}$ is given by the superposition of two waves $u_A$ and $u_B$, we have
\begin{aligned} u_C & =A_A \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{A C}+\phi_A-\omega t\right)\right]+A_B \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{B C}+\phi_B-\omega t\right)\right] \ & =\left{A_A \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{A C}+\phi_A\right)\right]+A_B \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{B C}+\phi_B\right)\right]\right} \exp (-\mathrm{i} \omega t) \end{aligned}

## 物理代写|光学工程代写Optical Engineering代考|FRINGE VISIBILITY

As the measure of interference fringe clarity, the contrast or the visibility is defined by
$$V=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }},$$
where $I_{\max }$ and $I_{\min }$ are the maximum and the minimum of the fringe intensity, respectively. We have
$$V=\frac{2 \sqrt{I_A I_B}}{I_A+I_B}$$ by using Eq. (2.9). The maximum contrast of $V=1$ is obtained when $I_A=I_B$. When either $I_A$ or $I_B$ is 0 , the minimum $V=0$ so that the fringe is invisible.

Whenever $A_A=A_B$, is the contrast always $V=1$ ? In reality, a special condition is necessary for $V=1$. The interference fringe exists stably in time, only when the difference $\phi_B-\phi_A$ of the initial phase of $\phi_A$ and $\phi_B$ at the point A and B is stable in time. The difference $\phi_B-\phi_A$ depends on the properties of the light sources, the distances from the light source to the point A and B, and so on. This means the contrast of the interference fringe depends not only on the path difference of $l_{B C}-l_{A C}$ but also the light source properties and the layout of the optical system.

The phase of wave from the light source in many cases is stable in less than $10^{-8}$ seconds. We can see the wave shape is sinusoidal only within this short time, where the amplitude and the phase are fixed within an appropriate time. Many wavelets with fixed duration generated from the light source form practical waves. From this concept, to generate a stable interference fringe at point $\mathrm{C}$, the waves A and B departing from the same source and at the same time should superimpose at point $\mathrm{C}$. The device used to perform such a superposition is called as an interferometer.
As described in Section 10.1, the stability of the phase difference $\phi_B-\phi_A$ depends on the properties of the light source. The measure is called the degree of coherence, $\gamma_{A B}$. We have $0 \leq \gamma_{A B} \leq 1$. In the case of $\gamma_{A B}=1$, two waves from the point $A$ and B are called coherent each other, and incoherent in the case of $\gamma_{A B}=0$. When considering the coherence, the fringe contract is rewritten as
$$V=\frac{2 \sqrt{I_A I_B}}{I_A+I_B} \gamma_{A B} .$$

# 光学工程代考

## 物理代写|光学工程代写Optical Engineering代考|Interference and Diffraction

$$u_A=A_A \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{A C}+\phi_A-\omega t\right)\right]$$

$$u_B=A_B \exp \left[\mathrm{i}\left(\frac{2 \pi}{\lambda_0} n l_{B C}+\phi_B-\omega t\right)\right],$$

## 物理代写|光学工程代写Optical Engineering代考|FRINGE VISIBILITY

$$V=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }},$$

$$V=\frac{2 \sqrt{I_A I_B}}{I_A+I_B}$$

$$V=\frac{2 \sqrt{I_A I_B}}{I_A+I_B} \gamma_{A B}$$

## 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|光学工程代写Optical Engineering代考|ES4C5

statistics-lab™ 为您的留学生涯保驾护航 在代写光学工程Optical Engineering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。我们的专家在代写光学工程Optical Engineering代写方面经验极为丰富，各种代写光学工程Optical Engineering相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|光学工程代写Optical Engineering代考|COMPLEX REPRESENTATION OF WAVE

In general, a plane wave is represented by Eq. (1.29), which is rewritten as
$$u(r, t)=\operatorname{Re}{A \exp [\mathrm{i}(k \cdot r-\omega t)]},$$
because
$$\exp (i \alpha)=\cos \dot{\alpha}+\mathrm{i} \sin \alpha,$$
where $\operatorname{Re}{\ldots}$ denotes the real part of complex number. Equation (1.36) is also represented by
\begin{aligned} u(r, t) & =\frac{1}{2}\left{A \exp [\mathrm{i}(k \cdot r-\omega t)]+A^* \exp [-\mathrm{i}(k \cdot r-\omega t)]\right} \ & =\frac{1}{2} A \exp [\mathrm{i}(k \cdot r-\omega t)]+\text { c.c., } \end{aligned}
where $A^*$ denotes the complex conjugate of $A$, and c.c. means the complex conjugate of its former term. In some cases, the symbol of the real part $\operatorname{Re}{\ldots}$ is omitted so that Eq. (1.36) is simply written as
$$u(r, t)=A \exp [\mathrm{i}(k \cdot r-\omega t)]$$

This is called the complex amplitude. It should be noted that a wave that exists physically is represented by a real number and so the complex amplitude is only a mathematical expression. We have introduced the complex amplitude for mathematical convenience. For example, to calculate a sum of waves
$$A=\sum_m A_m \exp \left[\mathrm{i}\left(k_m \cdot r-\omega t\right)\right]=\left[\sum_m A_m \exp \left(\mathrm{i} k_m \cdot r\right)\right] \cdot \exp (-\mathrm{i} \omega t)$$
we can separate a spatial part and a temporal part at first, and then calculate the spatial parts independently, and finally multiply the temporal part $\exp (-\mathrm{i} \omega t)$. The real amplitude is given by the real part of the final result. In many optical eases, only the spatial terms are considered. If necessary, the time-dependent term is multiplied with the final results of spatial calculation. It should be noted that such methods in the complex notation of wave are valid only in the case of linear operations.

## 物理代写|光学工程代写Optical Engineering代考|SCALAR WAVE AND VECTOR WAVE

Until now, we did not consider the direction of the electric field variation $u$. The light is an electromagnetic wave. Assuming the light is propagating to the direction of the $\mathrm{z}$ axis, the variation direction of the electric and magnetic fields are the directions of the $x$ and $y$ axes. This type of wave is called a transverse wave. On the other hand, an acoustic wave is a longitudinal wave, where the direction of variation is in the propagation direction $\mathrm{z}$.

In general, the electric field and the magnetic field are vectors with three components: $E\left(E_x, E_y, E_z\right)$ and $H\left(H_x, H_y, H_z\right)$, respectively. Therefore, the light wave propagation is vertical by nature.

In a homogeneous media, like vacuum, water or glass, the optical properties do not depend on the position and the propagation direction, and hence the components $E_x, E_y, E_z, H_x, H_y, H_z$ satisfy the wave equation independently:
$$\nabla^2 E_x=\frac{1}{v^2} \frac{\partial^2 E_x}{\partial t^2},$$

and so on. Those equations are integrated into the wave equation Eq. (1.11). This wave is called the scalar wave.

Generally, the light wave is considered as a scalar wave, but in an inhomogeneous media or near an aperture or boundary of homogeneous media, the components of electric and magnetic fields are not independent and interact with each other. In such a case, the scalar approximation is not valid and the light wave should be considered as a vector wave.

Next, consider a complex sinusoidal wave as a solution of scalar wave equation,
$$u(r, t)=U(r) \exp (-\mathrm{i} \omega t),$$
where
$$U(r)=A(r) \exp [\mathrm{i} \phi(r)] .$$
Since this equation satisfies the wave equation (1.11), substituting Eq. (1.50) into Eq. (1.11) gives the Helmholtz equation
$$\left(\nabla^2+k^2\right) U=0,$$
where $k$ denotes the wave number (1.14). The Helmholtz equation Eq. (1.52) describes the monochromatic wave propagation in a homogeneous medium.

# 光学工程代考

## 物理代写|光学工程代写Optical Engineering代考|COMPLEX REPRESENTATION OF WAVE

$$u(r, t)=\operatorname{Re} A \exp [\mathrm{i}(k \cdot r-\omega t)]$$

$$\exp (i \alpha)=\cos \dot{\alpha}+\mathrm{i} \sin \alpha$$

Ibegin ${$ aligned $} u(r, t) \&=\backslash f r a c{1}{2} \backslash \operatorname{left}\left{A\right.$ lexp $[\backslash m a t h r m{i}(k \backslash c$ dot $r-$ lomega $t)]+A^{\wedge} * \backslash \operatorname{lexp}[-\backslash m a t h r r$

$$u(r, t)=A \exp [\mathrm{i}(k \cdot r-\omega t)]$$

$$A=\sum_m A_m \exp \left[\mathrm{i}\left(k_m \cdot r-\omega t\right)\right]=\left[\sum_m A_m \exp \left(\mathrm{i} k_m \cdot r\right)\right] \cdot \exp (-\mathrm{i} \omega t)$$

## 物理代写|光学工程代写Optical Engineering代考|SCALAR WAVE AND VECTOR WAVE

$$\nabla^2 E_x=\frac{1}{v^2} \frac{\partial^2 E_x}{\partial t^2},$$

$$u(r, t)=U(r) \exp (-\mathrm{i} \omega t),$$

$$U(r)=A(r) \exp [\mathrm{i} \phi(r)] .$$

$$\left(\nabla^2+k^2\right) U=0,$$

## 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|光学工程代写Optical Engineering代考|CET824

statistics-lab™ 为您的留学生涯保驾护航 在代写光学工程Optical Engineering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。我们的专家在代写光学工程Optical Engineering代写方面经验极为丰富，各种代写光学工程Optical Engineering相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|光学工程代写Optical Engineering代考|WAVES AND THE WAVE EQUATION

Sound is the propagation of pressure variations or density changes of air. Light is the propagation of variation in the electric and magnetic fields.

Consider that the vibration $u$ propagates in the $z$ direction with the speed $v$, as shown in Fig. 1.1. Assuming the shape $f$ of the wave variation $u$ propagating in the $z$ direction at time $t=0$, we have
$$u(z, t=0)=f(z) .$$
The wave $u$ moves a distance $v t$ at time $t$ but its shape is not changed, so we have
$$u(z, t)=f(z-v t) .$$
This means that the wave variance does not change independently with variables of time $t$ and position $z$, but only as a function of $z-v t$. The relationship among variation $u$, position $z$ and time $t$ exists but does not depend on the shape of variation $f$. Using
$$\tau=z-v t$$
we have
\begin{aligned} & \frac{\partial u}{\partial z}=\frac{\partial u}{\partial \tau} \cdot \frac{\partial \tau}{\partial z}=\frac{\partial u}{\partial \tau} \ & \frac{\partial u}{\partial t}=\frac{\partial u}{\partial \tau} \cdot \frac{\partial \tau}{\partial t}=-v \frac{\partial u}{\partial \tau} \end{aligned}

Differentiating these again, we have
\begin{aligned} & \frac{\partial^2 u}{\partial z^2}=\frac{\partial}{\partial \tau}\left(\frac{\partial u}{\partial \tau}\right) \frac{\partial \tau}{\partial z}=\frac{\partial^2 u}{\partial \tau^2} \ & \frac{\partial^2 u}{\partial t^2}=\frac{\partial}{\partial \tau}\left(\frac{\partial u}{\partial \tau}\right) \frac{\partial \tau}{\partial t}=v^2 \frac{\partial^2 u}{\partial \tau^2} . \end{aligned}
Therefore we have
$$\frac{\partial^2 u}{\partial z^2}=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2} .$$
This equation describes the wave propagating in the $+z$ direction with the velocity $\pm v$. This is called the wave equation. ${ }^1$

In general, by extending Eq. (1.8), the wave equation in three dimensions $(x, y, z)$ can be written as
$$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2}=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2},$$
or by using the Laplacian operator
$$\nabla^2=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2},$$
the 3-D wave equation is rewritten as
$$\nabla^2 u=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2}$$

## 物理代写|光学工程代写Optical Engineering代考|PLANE WAVE

The most simple solution of the wave equation is a sinusoidal wave. The sinusoidal wave propagation to the $z$ direction with the velocity $v$ is written as
$$u(z, t)=A \cos [k(z-v t)+\phi] .$$
The equation evidently satisfies the wave equation (1.8). The maximum of variation $A$ is called the amplitude, and $k(z-v t)+\phi$ is the phase. The sinusoidal wave is a periodic function both in space and time, as shown in Fig. 1.2. The period in space is called the wavelength, denoted by $\lambda$. If the wave propagates a distance of $\lambda$, the phase of the wave in Eq. (1.12) changes by $2 \pi$;
$$k \lambda=2 \pi,$$
so we have
$$k=2 \pi / \lambda .$$
Since $k$ means a number of $\lambda$ in the length of $2 \pi$ and $k$ is called the wave number or propagation constant, in the field of optical wave guides, ${ }^2 \phi$ is initial phase and can be 0 , if the spatial coordinate $z$ and the time coordinate $t$ are arbitrary values.

The period $T$ in time is given by
$$T=\lambda / v$$
and the reciprocal of $T$ is frequency
$$v=1 / T .$$
Finally, we have the frequency
$$v=v / \lambda,$$
which means frequency is a number of waves per unit distance of $v$ (a propagation distance per unit time). The angular frequency is defined as
$$\omega=2 \pi v .$$
The light velocity in vacuum is a physical constant $c$. In the case of light wave, $v$ is light velocity in a medium. The ratio of $v$ and $c$ is refractive index $n$.
$$n=c / v .$$
The frequency is written as
$$v=c /(n \lambda)=c / \lambda_0,$$
where $\lambda_0$ denotes the light wavelength in vacuum. Therefore, $\lambda$ is wavelength in a medium, which is written as
$$\lambda=\lambda_0 / n$$

# 光学工程代考

## 物理代写|光学工程代写Optical Engineering代考|WAVES AND THE WAVE EQUATION

$$u(z, t=0)=f(z)$$

$$u(z, t)=f(z-v t)$$

$$\tau=z-v t$$

$$\frac{\partial u}{\partial z}=\frac{\partial u}{\partial \tau} \cdot \frac{\partial \tau}{\partial z}=\frac{\partial u}{\partial \tau} \quad \frac{\partial u}{\partial t}=\frac{\partial u}{\partial \tau} \cdot \frac{\partial \tau}{\partial t}=-v \frac{\partial u}{\partial \tau}$$

$$\frac{\partial^2 u}{\partial z^2}=\frac{\partial}{\partial \tau}\left(\frac{\partial u}{\partial \tau}\right) \frac{\partial \tau}{\partial z}=\frac{\partial^2 u}{\partial \tau^2} \quad \frac{\partial^2 u}{\partial t^2}=\frac{\partial}{\partial \tau}\left(\frac{\partial u}{\partial \tau}\right) \frac{\partial \tau}{\partial t}=v^2 \frac{\partial^2 u}{\partial \tau^2}$$

$$\frac{\partial^2 u}{\partial z^2}=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2}$$

$$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2}=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2}$$

$$\nabla^2=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2},$$
3-D波动方程重写为
$$\nabla^2 u=\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2}$$

## 物理代写|光学工程代写Optical Engineering代考|PLANE WAVE

$$u(z, t)=A \cos [k(z-v t)+\phi]$$

$$k \lambda=2 \pi,$$

$$k=2 \pi / \lambda$$

$$T=\lambda / v$$

$$v=1 / T$$

$$v=v / \lambda,$$

$$\omega=2 \pi v .$$

$$n=c / v \text {. }$$

$$v=c /(n \lambda)=c / \lambda_0,$$

$$\lambda=\lambda_0 / n$$

## 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。