### 数学代写|matlab代写|BMS13

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。

statistics-lab™ 为您的留学生涯保驾护航 在代写matlab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matlab代写方面经验极为丰富，各种代写matlab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

## 数学代写|matlab代写|Terminal velocity

As an object moves through a fluid, its viscosity resists the motion. Let us find the motion of a mass $m$ as it falls toward the earth under the force of gravity when the drag varies as the square of the velocity.
From Newton’s second law, the equation of motion is
$$m \frac{d v}{d t}=m g-C_{D} v^{2},$$
where $v$ denotes the velocity, $g$ is the gravitational acceleration, and $C_{D}$ is the drag coefficient. We choose the coordinate system so that a downward velocity is positive.

Equation 1.2.19 can be solved using the technique of separation of variables if we change from time $t$ as the independent variable to the distance traveled $x$ from the point of release. This modification yields the differential equation
$$m v \frac{d v}{d x}=m g-C_{D} v^{2},$$
since $v=d x / d t$. Separating the variables leads to
$$\frac{v d v}{1-k v^{2} / g}=g d x,$$
or
$$\ln \left(1-\frac{k v^{2}}{g}\right)=-2 k x,$$
where $k=C_{D} / m$ and $v=0$ for $x=0$. Taking the inverse of the natural logarithm, we finally obtain
$$v^{2}(x)=\frac{g}{k}\left(1-e^{-2 k x}\right) .$$
Thus, as the distance that the object falls increases, so does the velocity, and it eventually approaches a constant value $\sqrt{g / k}$, commonly known as the terminal velocity.

Because the drag coefficient $C_{D}$ varies with the superficial area of the object while the mass depends on the volume, $k$ increases as an object becomes smaller, resulting in a smaller terminal velocity. Consequently, although a human being of normal size will acquire a terminal velocity of approximately $120 \mathrm{mph}$, a mouse, on the other hand, can fall any distance without injury.

## 数学代写|matlab代写|Interest rate

Consider a bank account that has been set up to pay out a constant rate of $P$ dollars per year for the purchase of a car. This account has the special feature that it pays an annual interest rate of $r$ on the current balance. We would like to know the balance in the account at any time $t$.

Although financial transactions occur at regularly spaced intervals, an excellent approximation can be obtained by treating the amount in the account $x(t)$ as a continuous function of time governed by the equation
$$x(t+\Delta t) \approx x(t)+r x(t) \Delta t-P \Delta t,$$
where we have assumed that both the payment and interest are paid in time increments of $\Delta t$. As the time between payments tends to zero, we obtain the first-order ordinary differential equation
$$\frac{d x}{d t}=r x-P .$$
If we denote the initial deposit into this account by $x(0)$, then at any subsequent time
$$x(t)=x(0) e^{r t}-P\left(e^{r t}-1\right) / r .$$
Although we could compute $x(t)$ as a function of $P, r$, and $x(0)$, there are only three separate cases that merit our close attention. If $P / r>x(0)$, then the account will eventually equal zero at $r t=\ln {P /[P-r x(0)]}$. On the other hand, if $P / r<x(0)$, the amount of money in the account will grow without bound. Finally, the case $x(0)=P / r$ is the equilibrium case where the amount of money paid out balances the growth of money due to interest so that the account always has the balance of $P / r$.

## 数学代写|matlab代写|Terminal velocity

$$m \frac{d v}{d t}=m g-C_{D} v^{2},$$

$$m v \frac{d v}{d x}=m g-C_{D} v^{2},$$

$$\frac{v d v}{1-k v^{2} / g}=g d x$$

$$\ln \left(1-\frac{k v^{2}}{g}\right)=-2 k x$$

$$v^{2}(x)=\frac{g}{k}\left(1-e^{-2 k x}\right) .$$

## 数学代写|matlab代写|Interest rate

$$x(t+\Delta t) \approx x(t)+r x(t) \Delta t-P \Delta t$$

$$\frac{d x}{d t}=r x-P .$$

$$x(t)=x(0) e^{r t}-P\left(e^{r t}-1\right) / r .$$

## 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。