### 数学代写|matlab代写|CSC113

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|CLASSIFICATION OF DIFFERENTIAL EQUATIONS

Differential equations are classified three ways: by type, order, and linearity. There are two types: ordinary and partial differential equations, which have already been defined. Examples of ordinary differential equations include
$$\begin{gathered} \frac{d y}{d x}-2 y=x \ (x-y) d x+4 y d y=0 \ \frac{d u}{d x}+\frac{d v}{d x}=1+5 x \end{gathered}$$ and
$$\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+y=\sin (x) .$$
On the other hand, examples of partial differential equations include
$$\begin{gathered} \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0, \ y \frac{\partial u}{\partial x}+x \frac{\partial u}{\partial y}=2 u, \end{gathered}$$
and
$$\frac{\partial^{2} u}{\partial t^{2}}+2 \frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial x^{2}} .$$
In the examples that we have just given, we have explicitly written out the differentiation operation. However, from calculus we know that $d y / d x$ can also be written $y^{\prime}$. Similarly, the partial differentiation operator $\partial^{4} u / \partial x^{2} \partial y^{2}$ is sometimes written $u_{x x y y}$. We will also use this notation from time to time.

## 数学代写|matlab代写|SEPARATION OF VARIABLES

The simplest method of solving a first-order ordinary differential equation, if it works, is separation of variables. It has the advantage of handling both linear and nonlinear problems, especially autonomous equations. ${ }^{1}$ From integral calculus, we already met this technique when we solved the first-order differential equation
$$\frac{d y}{d x}=f(x) \text {. }$$

By multiplying both sides of Equation $1.2 .1$ by $d x$, we obtain
$$d y=f(x) d x .$$
At this point we note that the left side of Equation 1.2.2 contains only $y$ while the right side is purely a function of $x$. Hence, we can integrate directly and find that
$$y=\int f(x) d x+C .$$
For this technique to work, we must be able to rewrite the differential equation so that all of the $y$ dependence appears on one side of the equation while the $x$ dependence is on the other. Finally, we must be able to carry out the integration on both sides of the equation.
One of the interesting aspects of our analysis is the appearance of the arbitrary constant $C$ in Equation 1.2.3. To evaluate this constant, we need more information. The most common method is to require that the dependent variable give a particular value for a particular value of $x$. Because the independent variable $x$ often denotes time, this condition is usually called an initial condition, even in cases when the independent variable is not time.

## 数学代写|matlab代写|CLASSIFICATION OF DIFFERENTIAL EQUATIONS

$$\frac{d y}{d x}-2 y=x(x-y) d x+4 y d y=0 \frac{d u}{d x}+\frac{d v}{d x}=1+5 x$$

$$\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+y=\sin (x)$$

$$\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0, y \frac{\partial u}{\partial x}+x \frac{\partial u}{\partial y}=2 u$$

$$\frac{\partial^{2} u}{\partial t^{2}}+2 \frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial x^{2}}$$

## 数学代写|matlab代写|SEPARATION OF VARIABLES

$$\frac{d y}{d x}=f(x) .$$

$$d y=f(x) d x .$$

$$y=\int f(x) d x+C$$

## 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。