# 数学代写|数学建模代写Mathematical Modeling代考|SIMPLE SITUATIONS REQUIRING MATHEMATICAL MODELING

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## 数学代写|数学建模代写Mathematical Modeling代考|SIMPLE SITUATIONS REQUIRING MATHEMATICAL MODELING

(i) Find the height of a tower, say the Washington Monument or the leaning tower at Pisa (without climbing it!).
(ii) Find the width of a river or a canal (without crossing it!).
(iii) Find the mass of the Earth (without using a balance!).
(iv) Find the temperature at the surface or at the center of the Sun (without taking a thermometer there!).
(v) Estimate the yield of wheat in India from the standing crop (without cutting and weighing the whole of it!).
(vi) Find the volume of blood inside the body of a person (without bleeding him to death!).
(vii) Estimate the population of China in the year 2050 A.D. (without waiting till then!).
(viii) Find the time it takes a satellite at a height of $10,000 \mathrm{kms}$ above the Earth’s surface to complete one orbit (without sending such a satellite into orbit!).
(ix) Find the effect on the economy of a $30 \%$ reduction in income tax (without actually reducing the rate!).
(x) Find the gun with the best performance when the performance depends on ten parameters, each of which can take ten values (without manufacturing $10^{10}$ guns!).
(xi) Estimate the average life span of a light bulb manufactured in a factory (without lighting each bulb till it gets fused!).
(xii) Estimate the total amount of insurance claims a company has to pay next year (without waiting till the end of that year!).

All these problems and thousands of similar problems can be and have been solved through mathematical modeling.

One technique of solving the previous problems is similar to that of solving “word problems” in algebra. Suppose the age of a father is four times the age of his son and we are told that after five years, the age of the father will be only three times the age of the son. We have to find their ages. Let $x$ be the age of the father and $y$ be the age of the son, then the data of the problem gives
$$x=4 y, x+5=3(y+5)$$
giving $x=40, y=10$. The two equations of (1) give a mathematical model of the biological situation, so that the biological problem of ages is reduced to the mathematical problem of the solution of a system of two algebraic equations. The solution of the equations is finally interpreted biologically to give the ages of the father and the son.

In the same way to solve a given physical, biological, or social problem, we first develop a mathematical model for it, then solve the model and finally interpret the solution in terms of the original problem.

## 数学代写|数学建模代写Mathematical Modeling代考|THE TECHNIQUE OF MATHEMATICAL MODELING

Mathematical modeling essentially consists of translating real world problems into mathematical problems, solving the mathematical problems, and interpreting these solutions in the language of the real world (Figure 1.4).

This is expressed figuratively by saying that we catch hold of the real world problem in our teeth, dive into the mathematical ocean, swim there for some time, and we come out to the surface with the solution of the real world problem with us. Alternatively we may say that we soar high into the mathematical atmosphere along with the problem, fly there for some time, and come down to the Earth with the solution.

A real world problem in all its generality can seldom be translated into a mathematical problem, and even if it can be so translated, it may not be possible to solve the resulting mathematical problem. As such it is quite often necessary to “idealize” or “simply” the problem or approximate it by another problem which is quite close to the original problem and yet it can be translated and solved mathematically. In this idealization, we try to retain all the essential features of the problem, giving up those features which are not very essential or relevant to the situation we are investigating.

Sometimes the idealization assumptions may look quite drastic. Thus for considering the motions of planets, we may consider the planets and the Sun as point masses and neglect their sizes and structures. Similarly for considering the motion of a fluid, we may treat it as a continuous medium and neglect its discrete nature in terms of its molecular structure. The justification for such assumptions is often to be found in terms of the closeness of the agreement between observations and predictions of the mathematical models.

## 数学代写|数学建模代写Mathematical Modeling代考|SIMPLE SITUATIONS REQUIRING MATHEMATICAL MODELING

(i)找出一座塔的高度，比如华盛顿纪念碑或比萨斜塔(不用爬上去!)
(ii)找出一条河流或运河的宽度(不要越过它!)
(iii)求出地球的质量(不用天平!)
(iv)测量太阳表面或中心的温度(不要在那里使用温度计!)
(v)估计印度现有小麦的产量(不切割和称重)。
(六)测定一个人体内的血量(但不能使他流血致死!)
(vii)估计中国在公元2050年的人口(不用等到那个时候!)

(ix)找出所得税减少30%对经济的影响(实际上没有降低税率!)。
(x)当性能取决于10个参数时，找到性能最好的枪，每个参数可以取10个值(不制造$10^{10}$枪!)
(xi)估算工厂生产的灯泡的平均寿命(在熔断之前不点亮每个灯泡!)
(xii)估计公司明年必须支付的保险索赔总额(不要等到该年底!)


X =4 y X +5=3(y+5)


## 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。