Posted on Categories:数学代写, 数学建模

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## 数学代写|数学建模代写Mathematical Modeling代考|Use of analogies in the construction of models

Use of analogies in the construction of models. In plenty of cases where one is attempting to construct a model of a given object it is either impossible to specify directly the sought fundamental laws or variational principles, or, from the point of view of our present knowledge, there is no confidence in the existence of such laws admitting mathematical formulation. One of the fruitful approaches to such objects is to use analogies with already investigated phenomena. Indeed, what can be common between radioactive decay and the dynamics of populations, in particular, the change in the population of our planet? Even at the elementary level such an analogy is quite visible, as it is clear for one of the simplest models of population – the Malthus model. It is based on the simple assumption that the speed of change of the population in time $t$ is proportional to its current number $N(t)$, multiplied on the sum of factors of the birth $\alpha(t) \geq 0$ and the death rate $\beta(t) \leq 0$. As a result one comes to the equation
$$\frac{d N(t)}{d t}=[\alpha(t)-\beta(t)] N(t),$$
which is rather similar to the equation of radioactive decay and coinciding with it at $\alpha<\beta$ (if $\alpha$ and $\beta$ are constants). It is not surprising, since identical assumptions were made for their derivation. The integration of the equation (10) gives
$$N(t)=N(0) \exp \left(\int_{t_0}^t[\alpha(t)-\beta(t)] d t\right),$$
where $N(0)=N\left(t=t_0\right)$ is the initial population.

## 数学代写|数学建模代写Mathematical Modeling代考|Hierarchical approach to the construction of models

1. Hierarchical approach to the construction of models. Only in rare cases it is convenient and justified to construct complete mathematical models at once, even of quite simple objects, in view of all the factors essential for their behavior. Therefore it is natural to proceed in accordance to the principle “from the simple to the complex”, when the following step is made after the detailed study of models which are not too complex. Then, a chain (hierarchy) of more and more complete models is appearing, each of which generalizes the previous ones, including the former as a particular case.

Let us construct such a hierarchical chain on an example of a model of a multistage rocket. As was established at the end of Section 1, a real onestage rocket is unable to develop the first space speed. The reason is due to the amount of fuel to be used for the speeding up of the unnecessary parts of the structural mass of the rocket. Hence, with a movement of a rocket it is necessary to periodically get rid of a ballast. In terms of practical design it means that the rocket consists of several stages, which are discarded in the process of their use.

Let $m_i$ be the total mass of $i$-th stage, $\lambda m_i$ be the corresponding structural mass (so that the fuel mass is $\left.(1-\lambda) m_i\right), m_p$ be the mass of the useful loading. The value of $\lambda$ and speed of the escape of gases $u$ are the same for all stages. Consider for clarity the number of stages $n=3$. The initial mass of such a rocket is equal
$$m_0=m_p+m_1+m_2+m_3 .$$
Consider the moment when all the fuel of the first stage is spent and the mass of the rocket is equal
$$m_p+\lambda m_1+m_2+m_3 .$$
Then by the formula (6) of the initial model, the speed of the rocket equals
$$v_1=u \ln \left(\frac{m_0}{m_p+\lambda m_1+m_2+m_3}\right) .$$

## 数学代写|数学建模代写Mathematical Modeling代考|Use of analogies in the construction of models

$$\frac{d N(t)}{d t}=[\alpha(t)-\beta(t)] N(t)$$

$$N(t)=N(0) \exp \left(\int_{t_0}^t[\alpha(t)-\beta(t)] d t\right),$$

## 数学代写|数学建模代写Mathematical Modeling代考|Hierarchical approach to the construction of models

$$m_0=m_p+m_1+m_2+m_3$$

$$m_p+\lambda m_1+m_2+m_3$$

$$v_1=u \ln \left(\frac{m_0}{m_p+\lambda m_1+m_2+m_3}\right) .$$

## 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。

Posted on Categories:数学代写, 数学建模

## avatest™帮您通过考试

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## 数学代写|数学建模代写Mathematical Modeling代考|Data and Analysis

Data for the research presented here were collected in the first author’s grade $8(n=28)$ class while students worked on the aforementioned task. Although it is not possible to know if the grade 8’s had seen similar tasks in their previous years, this was one of the first of such tasks this group had been given in their grade 8 school year.

Students were randomly assigned to groups of 2-4 and worked on the task during a 75 min class. There were no instructions provided other than what can be seen in Fig. 9. While the students worked the teacher (first author) circulated naturally through the room and engaged in conversations with the students – sometimes prompted by her and sometimes prompted by the students.

These conversations were audio recorded and transcribed. At the same time photographs of student work were taken and students’ finished work was collected. These, coupled with field notes summarizing the interactions as well as observed student activity, allowed us to build cases for each group of students. Each of these cases is a narrative of their modelling experience punctuated by significant moments of activity and emotive expression. These cases constitute the data.

Given that natural and unscripted nature of the teacher’s movement through the room, not all of the cases are equally well documented. Regardless, each of these cases were analyzed separately through the lenses of modelling and flow. More specifically, the cases were analyzed using Borromeo Ferri’s (2006) modelling cycle as well as through Liljedahl’s (2018) modified theory of flow. The results of these disparate analyses were then combined and compared on an event by event basis to see if there were relationships between student engagement and various aspects of their modelling activities intersected.

In what follows we present one of the more complete and comprehensive of the aforementioned cases – the case of Amy and Angela. This is followed by the modelling cycle analysis, the flow analysis, and finally the joint modelling-flow analysis.

## 数学代写|数学建模代写Mathematical Modeling代考|Results and Discussion

Amy and Angela reacted to the modelling task by first asking questions about the parking lot. Amy believed that one of the key factors of the parking lot is the dimensions of a vehicle, and suggested to go outside to the staff parking lot to take some measurements.
Amy: How big is a car [talks to herself]? Can I go outside for a second [asks teacher]?

When she came back, Amy discussed these measurements with Angela, and suggested that they should increase these measurements to accommodate for large vehicles.
Amy: The car I measured was 2.5 metres by 1.5 metres, but it was a slightly smaller car so probably make it a bit bigger? ‘Cause there are bigger cars in the parking lot?
Angela: Like a Chevy.
Amy: What’s that?
Angela: It’s a truck.
After this conversation, Amy and Angela decided to put the parking lot on hold and investigated the possible locations and orientation of some of the building structures on the grid. First, they re-read the instructions provided, and paid attention to the areas on the grid which they were allowed to put buildings and the actual length each square represents. They divided 12.5 (distance between the border and all buildings) by 10 (each square represents $10 \mathrm{~m}$ ) and got “one and one-fourth”, and outlined a rectangle one and a quarter squares inside the border of the grid to represent the space they could put the buildings (see Fig. 10 for details).
Angela: So, all fields, courts, buildings, and parking lots must be no closer than 12.5 metres to any of the property lines. So one and one-fourth.

## 数学代写|数学建模代写Mathematical Modeling代考|Results and Discussion

Amy 和 Angela 对建模任务的反应是首先询问有关停车场的问题。艾米认为停车场的一个关键因素是车辆的尺寸，建议到外面的员工停车场测量一下。

) 得到“一又四分之一”，并在网格的边界内勾勒出一个四分之一的长方形，代表他们可以放置建筑物的空间（详见图 10）。

## 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。

Posted on Categories:数学代写, 数学建模

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 数学代写|数学建模代写Mathematical Modeling代考|Personal Epistemology: Epistemic Beliefs and Emotions

Personal epistemology is the study of people’s thinking about knowledge and about knowing. Its study is born in the field of educational and cognitive psychology (Barzilai and Zohar 2014; Hofer and Bendixen 2012; Hofer and Pintrich 1997). Even though in the last decades the field of personal epistemology has developed in several different directions there is convergence in some central descriptive dimensions of personal epistemology: the nature of knowledge, the certainty of knowledge, the simplicity of knowledge, the source of knowledge, and the justification of knowledge (Hofer and Pintrich 1997).

Currently there is no single model guiding research on personal epistemology (Bendixen and Rule 2004). We briefly present some of the approaches to the concept of personal epistemology that the perspective of educational psychology poses: approaches to development, approaches to beliefs and approaches to resources.

Developmental Approaches
Developmental models of personal epistemology generally view students as holding integrated epistemic positions or perspectives. These models describe students’ epistemic positions developing throughout the course of their life and studies, often following a typical trajectory (see Barzilai and Zohar 2014; Hofer and Pintrich 1997). Developmental approaches are concerned with identifying changes in students’ thinking. Thinking skills and theories about knowledge and knowing are deeply and intricately linked, capturing the close link between people’s views of knowledge and their reasoning processes by describing epistemic thinking as a “theory-in-action”. The developmental perspective encompasses both the epistemic reasoning processes and the epistemic beliefs and theories that underlie them. Beliefs reflect assumptions, expectations and attitudes that may affect reasoning processes.

Leder et al. (2002), Maass and Schloeglmann (2009), and Schoenfeld (1985) have conducted extensive research in the field of beliefs in mathematical education.
In this approach, personal epistemology is a term that refers to the beliefs that people hold about knowledge, both as to its nature and its acquisition and justification (Hofer 2002). Although different models of competence have been proposed, there is a consensus that epistemological beliefs refer to “belief about the nature of knowledge and knowledge processes” (Hofer and Pintrich 1997: 112) and in some cases learning (Op’t Eynde et al. 2006).

Epistemological beliefs have sometimes been explicitly described as a type of metacognitive knowledge or as schemas (Muis et al. 2015; Schoenfeld 1985). These models of epistemic beliefs and self-regulated learning are mainly concerned with understanding how and why epistemic beliefs impact learning and how they are conditions that serve as inputs to metalevel learning standards.

## 数学代写|数学建模代写Mathematical Modeling代考|Resources Approach

A third important approach to the study of personal epistemology is the resources approach (Elby and Hammer 2010). This perspective emerges from the “knowledge in pieces” approach to the study and analysis of knowledge, and highlights the fragmented and contextual nature of students’ epistemologies. Epistemological resources are specific cognitive resources highly linked to the context that people use to understand and reflect on their epistemic knowledge, activities and positions. Epistemological resources may gradually advance into beliefs as they become entirely articulated and more stable.

In the development of research, these approaches have often acted disjointedly, without taking into account, in an integrated way, that which each of them considers key components that underpin the concept of personal epistemology. One of the strongest criticisms of empirical studies on personal epistemology under these approaches to educational psychology is that they have little regard for the context and specific domains of knowledge (Bromme 2005 ).

In the field of Mathematical Education we must highlight authors who have adopted a different perspective and have implemented this epistemic integration, although not under the coined denomination of personal epistemology (Schoenfeld 2010, 2016). For example, Schoenfeld has worked with metacognition as a central aspect of cognition and has related it to belief systems (Schoenfeld 1987). The author has developed a theory of decision making, centred around teachers (Schoenfeld 2010). This work is indicative of the fact that in the field of Mathematics Education there is a fundamental and productive dialectic between theory and practice; and contextual and knowledge components, allowing for the development of observational tools for reliable naturalistic interventions in which classrooms can serve as laboratories.

## 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。