## 数学代写|微积分代写Calculus代写|MTH-211

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## 数学代写|微积分代写Calculus代写|ThE Growth OF KinEMatics IN thE WeST

Whereas in dynamics movement is studied in relation to the forces associated with it, in kinematics only its spatial and temporal aspects are considered. It follows that in kinematics we are concerned with the description of movement and not with its causes and it can therefore properly be regarded as the geometry of movement.

If a particle be known to trace a given curve the geometric properties of that curve can be used to predict the subsequent positions of the particle; conversely, if a curve be defined as the path of a point moving under specified conditions, then the laws of kinematics can be utilised to provide information as to certain geometric properties of the curve. For example, knowledge of the instantaneous motion at a given point on the curve enables us to draw the tangent to the curve at that point. The development, in the fourteenth century, of certain important concepts of motion including instantaneous velocity can therefore be seen to have direct and immediate bearing on the study of the tangent properties of curves. Furthermore, the introduction of graphical methods of representation led to the establishment of a link between the velocity-time graph, the total distance covered and the area under the curve, and this in turn is closely connected with the integral calculus (see Figs. 2.8 and 2.9).

The imaginative insights gained by the use of kinematic concepts in geometry were responsible for some of the more powerful methods developed during the seventeenth century for the study of curves. The work of Isaac Barrow, for instance, which certainly influenced Newton, is dominated by the idea of curves generated by moving points and lines.

## 数学代写|微积分代写Calculus代写|The Latitude OF Forms

At Merton College, Oxford, between the years 1328 and 1350, the distinction between kinematics and dynamics was made explicit. In the work of Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton the foundations for further study in this field were laid through the clarification and formalisation of a number of important concepts including the notion of instantaneous velocity (velocitas instantanea). ${ }^{\dagger}$

The study of space and motion at Merton College arose from the mediaeval discussion of the intension and remission of forms, i.e. the increase and decrease of the intensity of qualities. The distinction between intension and extension is exemplified in the case of heat by the difference between temperature, or degree of heat, and quantity of heat; in the case of weight between density, or weight per unit volume and total weight. For local motion the distinction is between velocity (or motion) at a given instant (instantaneous velocity) and total motion over a period of time, i.e. distance covered.

## 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。

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

Some atoms are unstable and can spontaneously emit mass or radiation. This process is called radioactive decay, and an element whose atoms go spontaneously through this process is called radioactive. Sometimes when an atom emits some of its mass through this process of radioactivity, the remainder of the atom re-forms to make an atom of some new element. For example, radioactive carbon-14 decays into nitrogen; radium, through a number of intermediate radioactive steps, decays into lead.

Experiments have shown that at any given time the rate at which a radioactive element decays (as measured by the number of nuclei that change per unit time) is approximately proportional to the number of radioactive nuclei present. Thus, the decay of a radioactive element is described by the equation $d y / d t=-k y, k>0$. It is conventional to use $-k$, with $k>0$, to emphasize that $y$ is decreasing. If $y_0$ is the number of radioactive nuclei present at time zero, the number still present at any later time $t$ will be
$$y=y_0 e^{-k t}, \quad k>0 .$$
The half-life of a radioactive element is the time expected to pass until half of the radioactive nuclei present in a sample decay. It is an interesting fact that the half-life is a constant that does not depend on the number of radioactive nuclei initially present in the sample, but only on the radioactive substance.

To compute the half-life, let $y_0$ be the number of radioactive nuclei initially present in the sample. Then the number $y$ present at any later time $t$ will be $y=y_0 e^{-k t}$. We seek the value of $t$ at which the number of radioactive nuclei present equals half the original number:
\begin{aligned} y_0 e^{-k t} & =\frac{1}{2} y_0 \ e^{-k t} & =\frac{1}{2} \ -k t & =\ln \frac{1}{2}=-\ln 2 \quad \text { Reciprocal Rule for logarithms } \ t & =\frac{\ln 2}{k} . \end{aligned}

## 数学代写|微积分代写Calculus代写|Heat Transfer: Newton’s Law of Cooling

Hot soup left in a tin cup cools to the temperature of the surrounding air. A hot silver bar immersed in a large tub of water cools to the temperature of the surrounding water. In situations like these, the rate at which an object’s temperature is changing at any given time is roughly proportional to the difference between its temperature and the temperature of the surrounding medium. This observation is called Newton’s Law of Cooling, although it applies to warming as well.

If $H$ is the temperature of the object at time $t$ and $H_S$ is the constant surrounding temperature, then the differential equation is
$$\frac{d H}{d t}=-k\left(H-H_S\right)$$
If we substitute $y$ for $\left(H-H_S\right)$, then
$$\begin{array}{rlrl} \frac{d y}{d t} & =\frac{d}{d t}\left(H-H_S\right)=\frac{d H}{d t}-\frac{d}{d t}\left(H_S\right) & \ & =\frac{d H}{d t}-0 & & \ & =\frac{d H}{d t} & & H_S \text { is a constant. } \ & =-k\left(H-H_S\right) & \ & =-k y . & & \text { Eq. (8) } \ & & H-H_S=y \end{array}$$
We know that the solution of the equation $d y / d t=-k y$ is $y=y_0 e^{-k t}$, where $y(0)=y_0$. Substituting $\left(H-H_S\right)$ for $y$, this says that
$$H-H_S=\left(H_0-H_S\right) e^{-k t},$$
where $H_0$ is the temperature at $t=0$. This equation is the solution to Newton’s Law of Cooling.

# 微积分代考

$$y=y_0 e^{-k t}, \quad k>0 .$$

## 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。