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数学代写|数学建模代写Mathematical Modeling代考|CLASSIFICATION OF MATHEMATICAL MODELS

如果你也在 怎样代写数学建模Mathematical Modeling这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。数学建模Mathematical Modeling是使用数学概念和语言对一个具体系统的抽象描述。建立数学模型的过程被称为数学建模。数学模型被用于自然科学(如物理学、生物学、地球科学、化学)和工程学科(如计算机科学、电气工程),以及非物理系统,如社会科学(如经济学、心理学、社会学、政治学)。使用数学模型来解决商业或军事行动中的问题是运筹学领域的一个重要部分。数学模型也被用于音乐、语言学、和哲学(例如,集中用于分析哲学)。

数学建模Mathematical Modeling可以有很多形式,包括动态系统、统计模型、微分方程或博弈论模型。这些和其他类型的模型可以重叠,一个特定的模型涉及各种抽象结构。一般来说,数学模型可能包括逻辑模型。在许多情况下,一个科学领域的质量取决于在理论方面开发的数学模型与可重复的实验结果的吻合程度。理论上的数学模型和实验测量结果之间缺乏一致性,往往导致更好的理论被开发出来,从而取得重要进展。

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数学代写|数学建模代写Mathematical Modeling代考|CLASSIFICATION OF MATHEMATICAL MODELS

数学代写|数学建模代写Mathematical Modeling代考|CLASSIFICATION OF MATHEMATICAL MODELS

(a) Mathematical models (MM) may be classified according to the subject matter of the models. Thus we have MM in physics (mathematical physics), MM in chemistry (theoretical chemistry), MM in biology (mathematical biology), MM in medicine (mathematical medicine), MM in economics (mathematical economics and econometrics), MM in psychology (mathematical psychology), MM in sociology (mathematical sociology), MM in engineering (mathematical engineering), and so on.
We similarly have MM of transportation, of urban and regional planning, of pollution, of environment, of oceanography, of blood flows, of genetics, of water resources, of optimal utilization of exhaustible and renewable resources, of political systems, of land distribution, of linguistics, and so on.
In fact every branch of knowledge has two aspects, one of which is theoretical, mathematical, statistical, and computer-based, and the other of which is empirical, experimental, and observational. Mathematical modeling is essential to the first of these two aspects. We have separate books on mathematical models in each of the areas we have mentioned previously and in many others. One can spend a lifetime specializing in mathematical models in one specified area alone.
(b) We may also classify mathematical models according to the mathematical techniques used in solving them. Thus we have mathematical modeling (MM) through classical algebra, MM through linear algebra and matrices, MM through ordinary and partial differential equations, MM through ordinary and partial difference equations, MM through integral equations, MM through intero-differential equations, MM through differential-difference equations, MM through functional equations, MM through graphs, MM through mathematical programming, MM through calculus of variations, MM through maximum principle, and so on.
Again, there are books on each of these techniques. However, in most of these books, most of the space is devoted to explaining the theory of the technique concerned and applications are given as illustrations only. The mathematical modeling aspect is seldom emphasized.
In books of category $(a)$, mathematical modeling is emphasized and techniques are considered of secondary importance (though this is not always the case) but the models belong to one specified field of knowledge. In books of category $(b)$, the theory of the technique is emphasized and ready-made models are used to illustrate the technique. In the present book, we assume the knowledge of the basic theory of each technique and lay emphasis mainly on mathematical modeling and applications of the technique. In particular we consider when models in terms of specific techniques may be relevant. Books of category $(a)$ consider applications of mathematics in one specified field of knowledge, but use a diversity of mathematical techniques. Books of category $(b)$ use a single technique, but consider application in a diversity of fields of knowledge. In the present book, we consider both a diversity of techniques and a diversity of fields of knowledge.
(c) Mathematical models may also be classified according to the purpose we have for the model. Thus we have mathematical models (MM) for description, MM for insight, MM for prediction, MM for organization, MM for control, and MM for action.
(d) Mathematical models may also be classified according to their nature. Thus
(i) Mathematical models may be linear or non-linear according to whether the basic equations describing them are linear or nonlinear.
(ii) Mathematical models may be static or dynamic according to whether or not the time variations in the system are taken into account.
(iii) Mathematical models may be deterministic or stochastic according to whether or not chance factors are taken into account.
(iv) Mathematical models may be discrete or continuous according to whether the variables involved are discrete or continuous.


(i) Realism of models: We want a mathematical model to be as realistic as possible and to represent reality as closely as possible. However, if a model is very realistic, it may not be mathematically tractable. In making a mathematical model, there has to be a trade-off between tractability and reality.
(ii) Hierarchy of models: Mathematical modeling is not a one-shot affair. Models are constantly improved to make them more realistic. Thus for every situation, we get a hierarchy of models, each more realistic than the preceding and each likely to be followed by a better one.
(iii) Relative precision of models: Different models differ in their precision and their agreement with observations.
(iv) Robustness of models: A mathematical model is said to be robust if small changes in the parameters lead to small changes in the behavior of the model. The decision is made by using sensitivity analysis for the models.
(v) Self-consistency of models: A mathematical model involves equations and inequations and these must be consistent, e.g., a model cannot have both $x+y>a$ and $x+y<a$. Sometimes the inconsistency results from inconsistency of basic assumptions. Since mathematical inconsistency is relatively easier to find out, this gives a method of finding inconsistency in requirements which social or biological scientists may require of their models. A well-known example of this is provided by Arrow’s impossibility theorem.
(vi) Oversimplified and overambitious models: It has been said that mathematics that is certain does not refer to reality and mathematics that refers to reality is not certain. A model may not represent reality because it is oversimplified. A model may also be overambitious in the sense that it may involve too many complications and may give results accurate to ten decimal places whereas the observations may be correct to two decimal places only.
(vii) Complexity of models: This can be increased by subdividing variables, by taking more variables and by considering more details. Increase of complexity need not always lead to increase of insight as after a stage, diminishing returns begin to set in. The art of mathematical modeling consists in stopping before this stage.
(viii) Models can lead to new experiments, new concepts, and new mathematics: Comparison of predictions with observations reveals the need for new experiments to collect needed data. Mathematical models can also lead to development of new concepts. If known mathematical techniques are not adequate to deduce results from the mathematical model, new mathematical techniques have to be developed.

数学代写|数学建模代写Mathematical Modeling代考|CLASSIFICATION OF MATHEMATICAL MODELS


数学代写|数学建模代写Mathematical Modeling代考|CLASSIFICATION OF MATHEMATICAL MODELS



(v)模型的自洽性:数学模型涉及方程和不等式,它们必须是一致的,例如,一个模型不能同时具有$x+y> A $和$x+y< A $。有时,不一致源于基本假设的不一致。由于数学上的不一致性相对容易发现,这就提供了一种方法来发现社会或生物科学家可能要求他们的模型的要求中的不一致性。一个著名的例子就是阿罗的不可能性定理。

数学代写|数学建模代写Mathematical Modeling代考

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微观经济学是主流经济学的一个分支,研究个人和企业在做出有关稀缺资源分配的决策时的行为以及这些个人和企业之间的相互作用。my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富,各种图论代写Graph Theory相关的作业也就用不着 说。




现代博弈论始于约翰-冯-诺伊曼(John von Neumann)提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理,这成为博弈论和数学经济学的标准方法。在他的论文之后,1944年,他与奥斯卡-莫根斯特恩(Oskar Morgenstern)共同撰写了《游戏和经济行为理论》一书,该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论,使数理统计学家和经济学家能够处理不确定性下的决策。


微积分,最初被称为无穷小微积分或 “无穷小的微积分”,是对连续变化的数学研究,就像几何学是对形状的研究,而代数是对算术运算的概括研究一样。

它有两个主要分支,微分和积分;微分涉及瞬时变化率和曲线的斜率,而积分涉及数量的累积,以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系,它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。





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。

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