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MATLAB是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

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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

## 数学代写|matlab代写|CAUCHY’S PRINCIPAL VALUE INTEGRAL

The conventional definition of the integral of a function $f(x)$ of the real variable $x$ over a finite interval $a \leq x \leq b$ assumes that $f(x)$ has definite finite value at each point within the interval. We shall now extend this definition to cover cases when $f(x)$ is infinite at a finite number of points within the interval.

Consider the case when there is only one point $c$ at which $f(x)$ becomes infinite. If $c$ is not an endpoint of the interval, we take two small positive numbers $\epsilon$ and $\eta$ and examine the expression
$$\int_{a}^{c-\epsilon} f(x) d x+\int_{c+\eta}^{b} f(x) d x .$$
If Equation 1.10.1 exists and tends to a unique limit as $\epsilon$ and $\eta$ tend to zero independently, we say that the improper integral of $f(x)$ over the interval exists, its value being defined by
$$\int_{a}^{b} f(x) d x=\lim {\epsilon \rightarrow 0} \int{a}^{c-\epsilon} f(x) d x+\lim {\eta \rightarrow 0} \int{c+\eta}^{b} f(x) d x .$$

If, however, the expression does not tend to a limit as $\epsilon$ and $\eta$ tend to zero independently, it may still happen that
$$\lim {\epsilon \rightarrow 0}\left{\int{a}^{c-\epsilon} f(x) d x+\int_{c+\epsilon}^{b} f(x) d x\right}$$
exists. When this is the case, we call this limit the Cauchy principal value of the improper integral and denote it by
$$P V \int_{a}^{b} f(x) d x .$$
Finally, if $f(x)$ becomes infinite at an endpoint, say $a$, of the range of integration, we say that $f(x)$ is integrable over $a \leq x \leq b$ if
$$\lim {\epsilon \rightarrow 0^{+}} \int{a+\epsilon}^{b} f(x) d x$$
exists.

## 数学代写|matlab代写|CONFORMAL MAPPING

Conformal mapping is a powerful technique for finding solutions, or for simplifying the process of finding solutions, to Laplace’s differential equation in two dimensions. This method involves introducing two complex variables: $z=x+i y$ and $\tau=\rho+i \sigma$. These two complex variables are related to each other via the mapping $z=f(\tau)$. Under this mapping the Argand diagram for the $z$-variable is mapped into one for the $\tau$-variable. In certain cases, for example $\tau=\sqrt{z}$, the complex $z$-plane may only map into a portion of the $\tau$-plane. In other cases, say $\tau=z+3 i$, the complete $z$-plane would be mapped into the complete $\tau$-plane.

Once we map the original domain into a simpler geometry (a half-plane, circle or square), how do we find the solution? There are several techniques available. One method, for example, recalls that the real and imaginary parts of an analytic function satisfy Laplacés équation. Therreforee, if wè could construct an analytic function whóse réal or imaginary parts satisfy the boundary conditions in the new domain, we would have the solution in the $\tau$-plane. Then we could use the transformation to obtain the solution in the original $z$-plane.

What types of functions $f(z)$ are useful? Consider an arbitrary point $z_{0}$ in the complex $z$-plane. Assuming that $f^{\prime}\left(z_{0}\right) \neq 0$, a straightforward transformation yields
$$\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}\right){z{0}}=\left|f^{\prime}\left(z_{0}\right)\right|^{2}\left(\frac{\partial^{2} v}{\partial \rho^{2}}+\frac{\partial^{2} v}{\partial \sigma^{2}}\right){\tau{0}},$$
where $u(x, y)$ and $v(\rho, \sigma)$ are solutions to Laplace’s equation in the $z$ and $\tau$ planes, respectively. Thus, $f(z)$ must be analytic.

# matlab代写

## 数学代写|matlab代写|CAUCHY’S PRINCIPAL VALUE INTEGRAL

$$\int_{a}^{c-\epsilon} f(x) d x+\int_{c+\eta}^{b} f(x) d x .$$

$$\int_{a}^{b} f(x) d x=\lim \epsilon \rightarrow 0 \int a^{c-\epsilon} f(x) d x+\lim \eta \rightarrow 0 \int c+\eta^{b} f(x) d x .$$

\eft 的分隔符缺失或无法识别

$$P V \int_{a}^{b} f(x) d x .$$

$$\lim \epsilon \rightarrow 0^{+} \int a+\epsilon^{b} f(x) d x$$

## 数学代写|matlab代写|CONFORMAL MAPPING

$$\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}\right) z 0=\left|f^{\prime}\left(z_{0}\right)\right|^{2}\left(\frac{\partial^{2} v}{\partial \rho^{2}}+\frac{\partial^{2} v}{\partial \sigma^{2}}\right) \tau 0,$$

## 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。

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