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# 数学代写|应用数学代考APPLIED MATHEMATICS代写|MATH311 Introduction – What is Applied Mathematics?

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## 数学代写|应用数学代考APPLIED MATHEMATICS代写|Introduction – What is Applied Mathematics?

Applied mathematics is a broad subject area dealing with the description, analysis, and prediction of real-world phenomena. It is more than a set of methods that can be used to solve equations that come from physics, engineering, and other applied sciences. In fact, applied mathematics also is about mathematical modeling and an entire process that intertwines with the physical reality. In this course, by a mathematical model (sometimes just called a model) we usually refer to an equation that describes some physical problem or phenomenon. Moreover, by mathematical modeling we mean the process of formulating, analyzing, and potentially refining a mathematical model. In particular, this process includes the following steps:

1. Introducing the relevant quantities or variables in the model
2. Solving the model by some (analytical or numerical) method
3. Comparing the solution of the model to real-world data and interpreting the results
4. If necessary, revising the model until it describes the underlying physical problem sufficiently accurate

Hence, mathematical modeling involves physical intuition, formulation of equations, solution methods, and analysis. Please note that solution methods can be both, of analytical or numerical nature. In this course, however, we will restrict ourselves to analytical methods (the ones involving the use of pen and paper) rather than using numerical methods (the ones involving the use of computers). Moreover, you (the student) are expected to already be familiar with basic solution methods for ordinary differential equations, which will be the class of mathematical models we will focus on in this course. Finally, let us – at least loosely – agree on what we demand from a ‘good’ model:

• It should be as simple as possible and as complex as necessary ${ }^1$
• It should apply to many situations
• It should be predictive

## 数学代写|应用数学代考APPLIED MATHEMATICS代写|Physical Dimensions and Units

Almost all physical quantities we will deal with in this course have a physical (or some other) dimension. Furthermore, this dimension is usually measured by using certain units. It is worth listing and getting familiar some of the more important dimensions and their corresponding units right from the start of this course. This will save us some trouble later on. Let us start by noting that there are two different classes of physical dimensions:

1. Basis dimensions (also called primary dimensions)
2. Derived dimensions (also called secondary dimensions)
As the name indicates, basis dimensions are defined independent or fundamental dimensions, from which other dimensions can be obtained. Table $2.1$ lists the seven basis dimensions as well as their corresponding symbols and units. We should note that there can be many possible units for measuring a certain dimension. For instance, length can be measured not just by the unit meter but also by millimeter, kilometer, inches, foot, mile, and many more. In this course, however, we will only use SI units (more commonly referred to as metric units) from the International System of Units (also Le Systeme International d’Unites) [oWMTT01]. The SI units corresponding to the seven basis dimensions can be found in Table $2.1$ as well.

# 应用数学代考

## 数学代写|应用数学代考APPLIED MATHEMATICS代写|Introduction – What is Applied Mathematics?

1. 在模型中引入相关量或变量
2. 通过某种（分析或数值）方法求解模型
3. 将模型的解决方案与真实世界的数据进行比较并解释结果
4. 如有必要，修改模型直到它足够准确地描述潜在的物理问题

• 它应该尽可能简单，必要时尽可能复杂1
• 它应该适用于许多情况
• 应该是有预见性的

## 数学代写|应用数学代考APPLIED MATHEMATICS代写|Physical Dimensions and Units

1. 基本尺寸（也称为主要尺寸）
2. 派生维度（也称为次级维度）
顾名思义，基础维度是定义独立的或基本的维度，从中可以得到其他维度。桌子2.1列出了七个基本维度及其相应的符号和单位。我们应该注意到，可以有许多可能的单位来衡量某个维度。例如，长度不仅可以用单位米来衡量，还可以用毫米、千米、英寸、英尺、英里等等来衡量。然而，在本课程中，我们将仅使用国际单位制（也称为 Le Systeme International d’Unites）[oWMTT01] 中的 SI 单位（通常称为公制单位）。七个基本维度对应的SI单位见表2.1以及。

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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。