澳洲代写｜ETC3250｜Introduction to machine learning机器学习入门 蒙纳士大学

statistics-labTM为您提供蒙纳士大学（Monash University）Introduction to machine learning机器学习入门澳洲代写代考辅导服务！

Business analytics involves uncovering the hidden information in masses of business data using statistical graphics, models and algorithms. The most widely used prediction and classification models will be covered. Practical skills in applying techniques to different problems will be developed using a suitable software environment that involves doing reproducible analyses. Topics to be covered include dimension reduction with methods such as principal component analysis, supervised learning with methods such as linear models, discriminant analysis, decision trees and forests, support vector machines, neural networks, and unsupervised methods such as k-means clustering. Techniques for numerical optimisation, Monte Carlo simulation, and resampling methods including bootstrap, cross-validation, and bagging will be discussed. Modelling will include nonlinear relationships and nonparametric methods.

Introduction to machine learning机器学习入门案例

Problem 1. Rademacher Complexities and beyond
Let $\mathcal{F}$ be a class of functions from $\mathcal{X}$ to $\mathbb{R}$ and let $X_1, \ldots, X_n$ be iid copies of a random variable $X \in \mathcal{X}$. Moreover, let $\sigma_1, \ldots, \sigma_n$ be $n$ i.i.d. $\operatorname{Rad}(1 / 2)$ random variables and let $g_1, \ldots, g_n$ be $n$ i.i.d. $N(0,1)$. Assume that all these random variables are mutually independent.

1. Prove the desymmetrization inequality:
$$\mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n \sigma_i\left[f\left(X_i\right)-\mathbb{E}[f(X)]\right]\right|\right] \leq 2 \mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n\left[f\left(X_i\right)-\mathbb{E}[f(X)]\right]\right|\right]$$

(1) Let $Y_1, \ldots, Y_n$ be ghost copies of $X_1, \ldots, X_n$. Then we have
\begin{aligned} \mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n \sigma_i\left[f\left(X_i\right)-\mathbb{E}[f(X)]\right]\right|\right] & =\mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n \sigma_i\left[f\left(X_i\right)-\mathbb{E}\left[f\left(Y_i\right)\right]\right]\right|\right] \ & \leq \mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n \sigma_i\left[f\left(X_i\right)-f\left(Y_i\right)\right]\right|\right] \end{aligned}
by Jensen’s inequality,
$$=\mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n\left[f\left(X_i\right)-f\left(Y_i\right)\right]\right|\right],$$
as $\sigma_i\left[f\left(X_i\right)-f\left(Y_i\right)\right]$ and $f\left(X_i\right)-f\left(Y_i\right)$ have the same distribution,
\begin{aligned} & =\mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n\left[\left(f\left(X_i\right)-\mathbb{E}\left[f\left(X_i\right)\right]\right)-\left(f\left(Y_i\right)-\mathbb{E}\left[f\left(Y_i\right)\right]\right)\right]\right|\right] \ & \leq 2 \mathbb{E}\left[\sup {f \in \mathcal{F}}\left|\frac{1}{n} \sum{i=1}^n\left[f\left(X_i\right)-\mathbb{E}\left[f\left(X_i\right)\right]\right]\right|\right] \end{aligned}
by the triangle inequality.

Prove the Rademacher/Gaussian process comparison inequality
$$\mathbb{E}\left[\sup {f \in \mathcal{F}} \sum{i=1}^n \sigma_i f\left(X_i\right)\right] \leq \sqrt{\frac{\pi}{2}} \mathbb{E}\left[\sup {f \in \mathcal{F}} \sum{i=1}^n g_i f\left(X_i\right)\right]$$
Define $R_n(\mathcal{F})=\mathbb{E}\left[\sup {f \in \mathcal{F}} \frac{1}{n}\left|\sum{i=1}^n \sigma_i f\left(X_i\right)\right|\right]$. Let $\mathcal{F}$ and $\mathcal{G}$ be two set of functions from $\mathcal{X}$ to $\mathbb{R}$ and recall that $\mathcal{F}+\mathcal{G}={f+g: f \in \mathcal{F}, g \in \mathcal{G}}$.

(2) The distribution of $g_i$ is the same as that of $\left|g_i\right| \sigma_i$, so we can write
\begin{aligned} \mathbb{E}\left[\sup {f \in \mathcal{F}} \sum{i=1}^n g_i f\left(X_i\right)\right] & =\mathbb{E}{X_i, \sigma_i}\left[\mathbb{E}{g_i}\left[\sup {f \in \mathcal{F}} \sum{i=1}^n\left|g_i\right| \sigma_i f\left(X_i\right) \mid X_i, \sigma_i\right]\right] \ & \geq \mathbb{E}{X_i, \sigma_i}\left[\sup {f \in \mathcal{F}} \sum_{i=1}^n \mathbb{E}\left[\left|g_i\right|\right] \sigma_i f\left(X_i\right)\right], \end{aligned}
by Jensen’s inequality,
$$=\sqrt{\frac{2}{\pi}} \mathbb{E}\left[\sup {f \in \mathcal{F}} \sum{i=1}^n \sigma_i f\left(X_i\right)\right],$$
using the first absolute moment of the standard Gaussian.

1. Let $h \in \mathbb{R}^{\mathcal{X}}$ be a given function and define $\mathcal{F}+h={f+h: f \in \mathcal{F}}$. Show that
$$R_n(\mathcal{F}+{h}) \leq R_n(\mathcal{F})+\frac{|h|_{\infty}}{\sqrt{n}},$$
where $|h|_{\infty}=\sup _{x \in \mathcal{X}}|h(x)|$.

(3) We compute:
\begin{aligned} R_n(\mathcal{F}+h) & =\mathbb{E}\left[\sup {f \in \mathcal{F}} \frac{1}{n}\left|\sum{i=1}^n \sigma_i\left(f\left(X_i\right)+h\left(X_i\right)\right)\right|\right] \ & \leq \mathbb{E}\left[\sup {f \in \mathcal{F}} \frac{1}{n}\left|\sum{i=1}^n \sigma_i f\left(X_i\right)\right|\right]+\mathbb{E}\left[\frac{1}{n}\left|\sum_{i=1}^n h\left(X_i\right)\right|\right], \end{aligned}
by the triangle inequality,
\begin{aligned} & =R_n(\mathcal{F})+\mathbb{E}\left[\frac{1}{n}\left|\sum_{i=1}^n h\left(X_i\right)\right|\right], \ & \leq R_n(\mathcal{F})+\frac{1}{n} \sqrt{\mathbb{E}\left[\left(\sum_{i=1}^n \sigma_i h\left(X_i\right)\right)^2\right]}, \end{aligned}
by Jensen’s inequality,
\begin{aligned} & =R_n(\mathcal{F})+\frac{1}{n} \sqrt{\sum_{i=1}^n \mathbb{E}\left[h\left(X_i\right)^2\right]+2 \sum_{i<j} \mathbb{E}\left[\sigma_i \sigma_j h\left(X_i\right) h\left(X_j\right)\right]} \ & =R_n(\mathcal{F})+\frac{1}{n} \sqrt{\sum_{i=1}^n \mathbb{E}\left[h\left(X_i\right)^2\right]} \end{aligned}
by symmetry,
\begin{aligned} & \leq R_n(\mathcal{F})+\frac{1}{n} \sqrt{n|h|_{\infty}^2} \ & =R_n(\mathcal{F})+\frac{|h|_{\infty}}{n} \end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

澳洲代写｜MTH3340 ｜Numerical methods for partial differential equations偏微分方程的数值方法 蒙纳士大学

statistics-labTM为您提供蒙纳士大学（Monash University）Numerical methods for partial differential equations偏微分方程的数值方法澳洲代写代考辅导服务！

Partial differential equations are ubiquitous in many domains of sciences and industry, as they model phenomena with spatial and temporal variations. Most of these models are too complex to be exactly solved, and numerical methods are the only way to gather quantitative behaviour on the solutions. This unit covers the design, analysis and implementation of numerical methods for partial differential equations. Topics covered can include finite difference methods, finite element methods, finite volume methods, error analysis, elliptic equations, parabolic equations, implementation in dynamic languages (such as Python or Julia). The focus will be on the design of the methods, their mathematical analysis, and their implementation and numerical testing.

Numerical methods for partial differential equations偏微分方程的数值方法案例

Solve $(z-y) p+(x-z) q=y-x$

Solution: The given equation is of the form $P p+Q q=R$.
Where, $P=z-y, Q=x-z$, and $R=y-x$
Now, the Langrage auxiliary equations are
$$\begin{gathered} \frac{d x}{P}=\frac{d y}{Q}=\frac{d z}{R} \ \frac{d x}{z-y}=\frac{d y}{x-z}=\frac{d z}{y-x} \end{gathered}$$
Add each fraction and compare with the last fraction, we can write
$$\begin{gathered} \frac{d x+d y+d z}{z-y+x-z+y-x}=\frac{d z}{y-x} \ \therefore \frac{d x+d y+d z}{0}=\frac{d z}{y-x} \ \therefore d x+d y+d z=0 \end{gathered}$$
Taking integration on both the sides
$$\therefore x+y+z=c_1$$
Hence, $u(x, y, z)=x+y+z=c_1$
For the second solution using $x, y$, and $z$ as multipliers and comparing with the last fraction, we get

$$\begin{gathered} \frac{x d x+y d y+z d z}{z x-y x+x y-z y+y z-x z}=\frac{d z}{y-x} \ \therefore \frac{x d x+y d y+z d z}{0}=\frac{d z}{y-x} \ \therefore x d x+y d y+z d z=0 \end{gathered}$$
Taking integration on both the sides
$$\therefore x^2+y^2+z^2=c_2$$
Hence, $v(x, y, z)=x^2+y^2+z^2=c_2$
Hence, the complete solution is given by
$$F\left[x+y+z, x^2+y^2+z^2\right]=0$$

Solve $\frac{\partial^2 z}{\partial x \partial y}=\sin x \sin y$, given that $\frac{\partial z}{\partial y}=-2 \sin y$, when $x=0$ and $z=0$, when $y$ is an odd multiple of $\frac{\pi}{2}$.

Solution: Given a partial differential equation is $\frac{\partial}{\partial x}\left(\frac{\partial z}{\partial y}\right)=\sin x \sin y$. Take integration on both the sides w.r.t., $x$ and consider $y$ as a constant.
$$\frac{\partial z}{\partial y}=-\cos x \sin y+f(y)$$
Now given that when $x=0 \Rightarrow \frac{\partial z}{\partial y}=-2 \sin y$

\begin{aligned} \therefore-2 \sin y & =-\cos 0 \sin y+f(y) \ \Rightarrow-2 \sin y & =-\sin y+f(y) \ \Rightarrow f(y) \quad & =-\sin y \ \therefore \frac{\partial z}{\partial y}= & -\cos x \sin y-\sin y \end{aligned}
Now, integrating both the sides w.r.t., $y$ and consider $x$ as a constant.
$$\therefore z=\cos x \cos y+\cos y+g(x)$$
Now, it is given that when $y$ is an odd multiple of $\frac{\pi}{2}$ then $z=0$.
That means if $y=(2 k+1) \frac{\pi}{2}, k=0, \pm 1, \pm 2 \ldots$ then $z=0$
\begin{aligned} & \therefore 0=\cos x \cos (2 k+1) \frac{\pi}{2}+\cos (2 k+1) \frac{\pi}{2}+g(x) \ & \Rightarrow g(x)=0 \end{aligned}
$\therefore z=\cos x \cos y+\cos y$ is the required solution.

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

澳洲代写｜MTH3360｜Fluid dynamics流体动力学 蒙纳士大学

statistics-labTM为您提供蒙纳士大学（Monash University）Fluid dynamics流体动力学澳洲代写代考辅导服务！

The continuum hypothesis; notion of a fluid particle; pathlines and streamlines. Eulerian and Lagrangian frameworks; the material derivative. Conservation of mass; incompressibility; streamfunctions. Forces acting on a fluid; the stress tensor; conservation of momentum; the constitutive relation; the incompressible Navier-Stokes equations. Boundary conditions. Exact solutions of Navier-Stokes equations. Non-dimensionalization and dimensional analysis; Reynolds number. Low Reynolds number flows. Vorticity; circulation; Helmholtz’ vorticity equation; properties of vorticity; Kelvin’s circulation theorem. Lubrication theory. Inviscid flows; potential flows. Boundary layer equations and flows.

Fluid dynamics流体动力学案例

A body weighs $1000 \mathrm{lbf}$ when exposed to a standard earth gravity $g=32.174 \mathrm{ft} / \mathrm{s}^2$. (a) What is its mass in $\mathrm{kg}$ ? (b) What will the weight of this body be in $\mathrm{N}$ if it is exposed to the moon’s standard acceleration $g_{\text {moon }}=1.62 \mathrm{~m} / \mathrm{s}^2$ ? (c) How fast will the body accelerate if a net force of $400 \mathrm{lbf}$ is applied to it on the moon or on the earth?

Solution
We need to find the (a) mass; $(b)$ weight on the moon; and (c) acceleration of this body. This is a fairly simple example of conversion factors for differing unit systems. No property data is needed. The example is too low-level for a sketch.

Newton’s law (1.2) holds with known weight and gravitational acceleration. Solve for $m$ :
$$F=W=1000 \mathrm{lbf}=m g=(m)\left(32.174 \mathrm{ft} / \mathrm{s}^2\right), \quad \text { or } \quad m=\frac{1000 \mathrm{lbf}}{32.174 \mathrm{ft} / \mathrm{s}^2}=31.08 \mathrm{slugs}$$
Convert this to kilograms:
$$m=31.08 \text { slugs }=(31.08 \text { slugs })(14.5939 \mathrm{~kg} / \mathrm{slug})=454 \mathrm{~kg} \quad \text { Ans. }(\text { a })$$
The mass of the body remains $454 \mathrm{~kg}$ regardless of its location. Equation (1.2) applies with a new gravitational acceleration and hence a new weight:
$$F=W_{\text {moon }}=m g_{\text {moon }}=(454 \mathrm{~kg})\left(1.62 \mathrm{~m} / \mathrm{s}^2\right)=735 \mathrm{~N}$$
This part does not involve weight or gravity or location. It is simply an application of Newton’s law with a known mass and known force:
$$F=400 \mathrm{lbf}=m a=(31.08 \text { slugs }) a$$
Solve for
$$a=\frac{400 \mathrm{lbf}}{31.08 \text { slugs }}=12.87 \frac{\mathrm{ft}}{\mathrm{s}^2}\left(0.3048 \frac{\mathrm{m}}{\mathrm{ft}}\right)=3.92 \frac{\mathrm{m}}{\mathrm{s}^2}$$
Ans. (c)
Comment $(c)$ : This acceleration would be the same on the earth or moon or anywhere.

Industries involved in viscosity measurement $[27,36]$ continue to use the CGS system of units, since centimeters and grams yield convenient numbers for many fluids. The absolute viscosity $(\mu)$ unit is the poise, named after J. L. M. Poiseuille, a French physician who in 1840 performed pioneering experiments on water flow in pipes; 1 poise $=1 \mathrm{~g} /(\mathrm{cm}-\mathrm{s})$. The kinematic viscosity $(\nu)$ unit is the stokes, named after G. G. Stokes, a British physicist who in 1845 helped develop the basic partial differential equations of fluid momentum; 1 stokes $=1 \mathrm{~cm}^2 / \mathrm{s}$. Water at $20^{\circ} \mathrm{C}$ has $\mu \approx 0.01$ poise and also $\nu \approx 0.01$ stokes. Express these results in (a) SI and (b) BG units.

Solution

• Approach: Systematically change grams to $\mathrm{kg}$ or slugs and change centimeters to meters or feet.
• Property values: Given $\mu=0.01 \mathrm{~g} /(\mathrm{cm}-\mathrm{s})$ and $\nu=0.01 \mathrm{~cm}^2 / \mathrm{s}$.
• Solution steps: (a) For conversion to SI units,
\begin{aligned} & \mu=0.01 \frac{\mathrm{g}}{\mathrm{cm} \cdot \mathrm{s}}=0.01 \frac{\mathrm{g}(1 \mathrm{~kg} / 1000 \mathrm{~g})}{\mathrm{cm}(0.01 \mathrm{~m} / \mathrm{cm}) \mathrm{s}}=0.001 \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}} \ & \nu=0.01 \frac{\mathrm{cm}^2}{\mathrm{~s}}=0.01 \frac{\mathrm{cm}^2(0.01 \mathrm{~m} / \mathrm{cm})^2}{\mathrm{~s}}=0.000001 \frac{\mathrm{m}^2}{\mathrm{~s}} \end{aligned}
Ans. (a)
• For conversion to BG units
\begin{aligned} & \mu=0.01 \frac{\mathrm{g}}{\mathrm{cm} \cdot \mathrm{s}}=0.01 \frac{\mathrm{g}(1 \mathrm{~kg} / 1000 \mathrm{~g})(1 \mathrm{slug} / 14.5939 \mathrm{~kg})}{(0.01 \mathrm{~m} / \mathrm{cm})(1 \mathrm{ft} / 0.3048 \mathrm{~m}) \mathrm{s}}=0.0000209 \frac{\mathrm{slug}}{\mathrm{ft} \cdot \mathrm{s}} \ & \nu=0.01 \frac{\mathrm{cm}^2}{\mathrm{~s}}=0.01 \frac{\mathrm{cm}^2(0.01 \mathrm{~m} / \mathrm{cm})^2(1 \mathrm{ft} / 0.3048 \mathrm{~m})^2}{\mathrm{~s}}=0.0000108 \frac{\mathrm{ft}^2}{\mathrm{~s}} \quad \text { An } \end{aligned}
• Comments: This was a laborious conversion that could have been shortened by using the direct viscosity conversion factors in App. C. For example, $\mu_{\mathrm{BG}}=\mu_{\mathrm{SI}} / 47.88$.

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

澳洲代写｜ECE3121｜Engineering electromagnetics 电磁工程学 蒙纳士大学

statistics-labTM为您提供蒙纳士大学（Monash University）Engineering electromagnetics 电磁工程学澳洲代写代考辅导服务！

This unit explores electrostatic, magnetostatic and electromagnetic fields, and their use to create devices and systems. Mathematical concepts are used to describe the fields, and examine the basic laws governing the generation of fields and their interactions with dielectric and magnetic materials. This study results in Maxwell’s field equations, and related Laplace, Poisson and continuity equations. The real life applications of electromagnetic fields in radio communications and devices such as scanners, printers and mass spectrometers are also explored in this unit. Finally, plane wave propagation is analysed briefly as an extension of Maxwell’s field equations.

Engineering electromagnetics 电磁工程学定义

Work in a Field A vector field is given as $\mathbf{F}=\hat{\mathbf{x}} 2 x+\hat{\mathbf{y}} 2 y$.
(a) Sketch the field in space.

Solution: (b) First, we calculate the line integral of $\mathbf{F} \cdot d \mathbf{l}$ along the path between $P_2$ and $P_3$. This is a direct path. (c) Then, we calculate the same integral from $P_2$ to $P_1$ and from $P_1$ to $P_3$. If the two results are the same, the closed contour integral is zero.

(b) Assume $\mathbf{F}$ is a force. What is the work done in moving from point $P_2(5,0)$ to $P_3(0,3)$

(b) From $P_2$ to $P_3$, the element of path is $d \mathbf{l}=\hat{\mathbf{x}} d x+\hat{\mathbf{y}} d y$. The integration is therefore
$$\int_{P_2}^{P_3} \mathbf{F} \cdot d \mathbf{l}=\int_{P_2}^{P_3}(\hat{\mathbf{x}} 2 x+\hat{\mathbf{y}} 2 y) \cdot(\hat{\mathbf{x}} d x+\hat{\mathbf{y}} d y)=\int_{P_2}^{P_3}(2 x d x+2 y d y)$$
Since each part of the integrand is a function of a single variable, $x$ or $y$, we can separate the integration into integration over each variable and write
$$\int_{P_2}^{P_3} \mathbf{F} \cdot d \mathbf{l}=\int_{x=5}^{x=0} 2 x d x+\int_{y=0}^{y=3} 2 y d y=\left.x^2\right|_5 ^0+\left.y^2\right|_0 ^3=-25+9=-16$$

(c) Does the work depend on the path taken between $P_2$ and $P_3$ ?

(c) On paths $P_2$ to $P_1$ and $P_1$ to $P_3$, we perform separate integrations. On path $P_2$ to $P_1, d \mathbf{l}=\hat{\mathbf{x}} d x+\hat{\mathbf{y}} 0$ and $y=0$. The integration is
$$\int_{P_2}^{P_1} \mathbf{F} \cdot d \mathbf{l}=\int_{P_2}^{P_1}(\hat{\mathbf{x}} 2 x+\hat{\mathbf{y}} 2 y) \cdot(\hat{\mathbf{x}} d x)=\int_{P_2}^{P_1} 2 x d x=\int_{x=5}^{x=0} 2 x d x=\left.x^2\right|5 ^0=-25 \quad[\mathbf{J}]$$ Similarly, on path $P_1$ to $P_3, d \mathbf{l}=\hat{\mathbf{x}} 0+\hat{\mathbf{y}} d y$ and $x=0$. The integration is $$\int{P_1}^{P_3} \mathbf{F} \cdot d \mathbf{l}=\int_{P_1}^{P_3}(\hat{\mathbf{x}} 2 x+\hat{\mathbf{y}} 2 y) \cdot(\hat{\mathbf{y}} d y)=\int_{P_1}^{P_3} 2 y d y=\int_{y=0}^{y=3} 2 y d y=\left.y^2\right|_0 ^3=9$$
The sum of the two paths is equal to the result obtained for the direct path. This also means that the closed contour

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PCS624

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$$\int_{-\infty}^{+\infty} e^{-x^2} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)+R_n$$
On neglecting the remainder term, it can be written as
$$\int_{-\infty}^{+\infty} e^{-x^2} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)$$
The alternative form of the above equation is
$$\int_{-\infty}^{+\infty} g(x) d x=\sum_{i=1}^n w_i e^{x_i^2} g\left(x_i\right)$$
In Equations 9.8a through 9.8c, $x_i$ is the $i$ th zero of $H_n(x), H_n(x)$ is the Hermite polynomials, $w_i$ is the weight and $R_n$ is the remainder
$$\begin{gathered} w_i=\frac{2^{n-1} n ! \sqrt{\pi}}{n^2\left[H_{n-1}\left(x_i\right)\right]^2} \ R_n=\frac{n ! \sqrt{\pi}}{2^n(2 n) !} f^{2 n}(\xi) \quad(-\infty<\xi<\infty) \end{gathered}$$
The weight factors $\left(w_i\right)$ and the product $w_i e^{x_i{ }^2}$ for the values of abscissas $\left(x_i\right)$ representing zeros of Hermite polynomials are available ${ }^{14}$ for $n=2,3,4,5,6$, $7,8,9,10,12,16$ and 20 . Table 9.1 gives these values for an arbitrarily selected $n(=9)$.

$$\int_0^{+\infty} e^{-x} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)+R_n$$
On neglecting the remainder term, it can be written as
$$\int_0^{+\infty} e^{-x} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)$$
The above equation can be written in the following alternative form:
$$\int_0^{+\infty} g(x) d x=\sum_{i=1}^n w_i e^{x_i} g\left(x_i\right)$$

In Equations 9.10 through $9.10 \mathrm{c}, x_i$ is the $i$ th zero of $L_n(x), L_n(x)$ is the Laguerre polynomials, $w_i$ is the weight and $R_n$ is the remainder
$$\begin{gathered} w_i=\frac{(n !)^2 x_i}{(n+1)^2\left[L_{n+1}\left(x_i\right)\right]^2} \ R_n=\frac{(n !)^2}{(2 n) !} f^{2 n}(\xi) \quad(0<\xi<\infty) \end{gathered}$$
Weight factors $\left(w_i\right)$ and the product $w_i e^{x_i}$ for some selected values of abscissas $\left(x_i\right)$ representing zeros of Laguerre polynomials are available ${ }^{14}$ for $n=2,3,4,5,6$, $7,8,9,10,12$ and 15 . Table 9.2 gives these values for an arbitrarily selected $n(=9)$.

物理代写|电磁学代写electromagnetism代考|Change of Variable for Infinite Intervals

If, in Equation 9.8a, $x$ is replaced by $t /\left(1-t^2\right)$, then $d x=\left(\left(1+t^2\right) /\left(1-t^2\right)^2\right)$. In view of this replacement the limits of ‘ $-\infty$ ‘ to ‘ $+\infty$ ‘ change to ‘ -1 ‘ to ‘ +1 ‘. Thus, the integral of infinite interval reduces to that of finite interval
$$\int_{-\infty}^{+\infty} f(x) d x=\int_{-1}^{+1} f\left(\frac{t}{1-t^2}\right) \frac{1+t^2}{\left(1-t^2\right)^2} d t$$

In this case, $x$ is replaced by $a+(t /(1-t))$ then $d x=d t /(1-t)^2$ and the limits ‘ $a$ ‘ to ‘ $\infty$ ‘ change from ‘ 0 ‘ to ‘ 1 ‘. Thus, the integral becomes
$$\int_a^{+\infty} f(x) d x=\int_0^1 f\left(a+\frac{t}{1-t}\right) \frac{d t}{(1-t)^2}$$

Here $x$ is replaced by $a-((1-t) / t)$ then $d x=d t / t^2$ and the limits ‘ $\infty$ ‘ to ‘ $a$ ‘ change to ‘ 0 ‘ to ‘ 1 ‘. The integral thus becomes
$$\int_{-\infty}^a f(x) d x=\int_0^1 f\left(a-\frac{1-t}{t}\right) \frac{d t}{t^2}$$

The quadrature rules as such are designed to compute one-dimensional integrals. The multi-dimensional integrals can, however, also be evaluated by repeating one-dimensional integrals. In this approach, the function evaluations exponentially grow with the number of dimensions and some methods to overcome this effect are to be used. Monte Carlo or quasi-Monte Carlo methods provide better alternatives. These methods are easy to apply to multi-dimensional integrals. Besides, these may yield greater accuracy for the same number of function evaluations than repeated integrations using one-dimensional methods. Markov chain Monte Carlo algorithms, which include Metropolis-Hestings algorithm and Gibbs sampling, belong to a large class of useful Monte Carlo methods. Besides, sparse grids are developed by Smolyak for the quadrature of high-dimensional functions. Although it is based on a one-dimensional quadrature rule, it performs more sophisticated combination of univariate results.

电磁学代考

$$\int_{-\infty}^{+\infty} e^{-x^2} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)+R_n$$

$$\int_{-\infty}^{+\infty} e^{-x^2} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)$$

$$\int_{-\infty}^{+\infty} g(x) d x=\sum_{i=1}^n w_i e^{x_i^2} g\left(x_i\right)$$

$$\begin{gathered} w_i=\frac{2^{n-1} n ! \sqrt{\pi}}{n^2\left[H_{n-1}\left(x_i\right)\right]^2} \ R_n=\frac{n ! \sqrt{\pi}}{2^n(2 n) !} f^{2 n}(\xi) \quad(-\infty<\xi<\infty) \end{gathered}$$

$$\int_0^{+\infty} e^{-x} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)+R_n$$

$$\int_0^{+\infty} e^{-x} f(x) d x=\sum_{i=1}^n w_i f\left(x_i\right)$$

$$\int_0^{+\infty} g(x) d x=\sum_{i=1}^n w_i e^{x_i} g\left(x_i\right)$$

$$\begin{gathered} w_i=\frac{(n !)^2 x_i}{(n+1)^2\left[L_{n+1}\left(x_i\right)\right]^2} \ R_n=\frac{(n !)^2}{(2 n) !} f^{2 n}(\xi) \quad(0<\xi<\infty) \end{gathered}$$

物理代写|电磁学代写electromagnetism代考|Change of Variable for Infinite Intervals

$$\int_{-\infty}^{+\infty} f(x) d x=\int_{-1}^{+1} f\left(\frac{t}{1-t^2}\right) \frac{1+t^2}{\left(1-t^2\right)^2} d t$$

$$\int_a^{+\infty} f(x) d x=\int_0^1 f\left(a+\frac{t}{1-t}\right) \frac{d t}{(1-t)^2}$$

$$\int_{-\infty}^a f(x) d x=\int_0^1 f\left(a-\frac{1-t}{t}\right) \frac{d t}{t^2}$$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PHYS355

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物理代写|电磁学代写electromagnetism代考|Numerical Analysis

Numerical analysis is the study of algorithms that use numerical approximation for the mathematical problems that evolve out of some physical systems or processes. Its overall goal is the design and analysis of techniques to give approximate but acceptable solutions to the complicated problems. These problems may be related to weather predictions, computation of the trajectories of spacecraft, the crash safety of cars, stresses developed in physical structures or the distribution of fields and so on. For estimating trajectories, the accurate numerical solution of a system of ordinary differential equations may be required, whereas car safety may require numerical solutions of partial differential equations. The problem of structure or that of fields may also involve ordinary or partial differential equations, integral equations and so on.

In numerical analysis, the process of interpolation, extrapolation and regression are quite frequently employed. In case of interpolation, the value of some unknown function can be evaluated in between the two given values of the function. In extrapolation, the value of some unknown function is to be evaluated, which falls outside the given points. This process first assesses the nature of variation of previous values and based on this trend estimates the new values. Regression is also a similar process, but it takes into account that the data are imprecise. Given some points, and a measurement of the value of some function at these points (with an error), it determines the unknown function. It mostly relies on the least square error to achieve the goal.
9.2.1 Computational Errors
No technique, which falls in the domain of numerical analysis, is error free. These errors creep in mainly due to the following reasons:

1. In general, all practical computers have a finite memory and it is impossible to exactly represent all the real numbers on such a computing machine. Thus, a class of error referred to as the round-off errors are bound to occur.
2. When an iterative method is terminated or a mathematical procedure is approximated, the error due to which the approximate solution differs from the exact solution is referred to as truncation errors.
3. Similarly, the discretisation induces a discretisation error because the solution of the discrete problem does not coincide with the solution of the continuous problem.
It may be noted that once an error is generated, it generally propagates through subsequent calculations.

物理代写|电磁学代写electromagnetism代考|Domain of Numerical Analysis

The field of numerical analysis includes many subdisciplines and encompasses problems of multi-facial nature. These may include the following.

The evaluation of a function at a given point is one of the simplest problems. In the case of polynomials, the Horner scheme is a better approach, since it requires a lesser number of multiplications and additions. In this case, the estimation and control of round-off errors due to the use of floating point arithmetic is of immense importance.

These can be further classified into linear and nonlinear forms. Linear equations are an important class of the numerical analysis. There are many methods for solving the systems of linear equations. Some standard methods employ matrix decomposition techniques. These include Gaussian elimination, LU (lower-upper) decomposition, Cholesky decomposition for symmetric (or Hermitian) and positive-definite matrix and QR decomposition for nonsquare matrices. For large systems preference is given to iterative methods, which include Jacobi method, Gauss-Seidel method, successive over relaxation method and conjugate gradient method. General iterative methods can be developed by using a matrix splitting.

Nonlinear equations are solved by using root-finding algorithms. In this case, if the function is differentiable and the derivative is known it can be solved by using Newton’s method. The technique referred to as linearisation can also be employed for solving nonlinear equations.

In context to the system of equations, it seems to be appropriate to describe the formation of matrices from linear algebraic equations. An algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable is referred to as a linear equation. A linear equation can involve a number of variables but does not include exponents. An equation involving $n$ variables can be written in the following form:
$$a_1 x_1+a_2 x_2+\cdots+a_n x_n=b$$
where $a_1, a_2, \ldots, a_n$ represent numbers and are called the coefficients. The parameters $x_1, x_2, \ldots, x_n$ are the unknowns and $b$ is called the constant term. The present analysis gives rise to a set of such equations, which can be written as
$$\begin{gathered} A_{11} x_1+a_{12} x_2+\cdots+a_{1 N} x_N=b_1 \ A_{21} x_1+a_{22} x_2+\cdots+a_{2 N} x_N=b_2 \ \cdots \ A_{M 1 x 1}+a_{M 2} x_2+\cdots+a_{M N} x_N=b_M \end{gathered}$$

电磁学代考

9.2.1计算误差

物理代写|电磁学代写electromagnetism代考|Domain of Numerical Analysis

$$a_1 x_1+a_2 x_2+\cdots+a_n x_n=b$$

$$\begin{gathered} A_{11} x_1+a_{12} x_2+\cdots+a_{1 N} x_N=b_1 \ A_{21} x_1+a_{22} x_2+\cdots+a_{2 N} x_N=b_2 \ \cdots \ A_{M 1 x 1}+a_{M 2} x_2+\cdots+a_{M N} x_N=b_M \end{gathered}$$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PHYSICS7536

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物理代写|电磁学代写electromagnetism代考|Power Components

Equation 8.76 a contains the following four components:
$$\begin{gathered} \mathcal{P}{H L}=(s \cdot \omega) \cdot \frac{1}{2} \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right) \ \mathcal{P}{E L}=\frac{1}{2} \cdot \frac{1}{\sigma_1} J{1 x} \cdot J_{1 x}^* \ \mathcal{P}{E M}=u_y \cdot \frac{1}{2} \alpha \cdot \mathcal{R} e\left[-e^{-j \beta} J{1 x}^* \cdot H_{1 z}\right] \ \mathcal{P}{H M}=u_y \cdot \frac{1}{2} \ell \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right) \end{gathered}$$
These four terms bear the following meaning:

1. The first term $\left(\mathcal{P}_{H L}\right.$ ) given by Equation $8.76 \mathrm{~b}$ represents the power density proportional to the slip frequency. For hysteresis-free media, this term is zero. Therefore, it can be considered as hysteresis loss per unit volume of the rotor ring.
2. The second term $\left(\mathcal{P}_{E L}\right)$ given by Equation $8.76 \mathrm{c}$ represents the eddy current loss per unit rotor ring volume. This term vanishes for zero conductivity resulting in the absence of eddy currents.
3. The third term $\left(\mathcal{P}_{E M}\right)$ is due to eddy currents in the rotor ring. As it is proportional to the rotor speed, it indicates the mechanical power developed due to induction machine action.
4. The fourth term $\left(\mathcal{P}_{H M}\right)$ is also proportional to the rotor speed and thus indicates the mechanical power developed due to hysteresis machine action. This term vanishes for zero value of the hysteretic angle, $\beta$.

物理代写|电磁学代写electromagnetism代考|Slip-Power Relation

From Equations $8.76 \mathrm{~b}$ and $8.76 \mathrm{e}$, we get
$$\frac{\mathcal{P}{H M}}{\mathcal{P}{H L}}=\frac{1-s}{s}$$
The total hysteretic power is given as
$$\mathcal{P}H=\mathcal{P}{H L}+\mathcal{P}{H M}=\frac{1}{2} \cdot \omega \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right)$$
For a hysteresis machine with zero conductivity of the rotor, this term in view of Equations $8.57 \mathrm{c}, 8.58 \mathrm{a}, 8.58 \mathrm{~b}, 8.58 \mathrm{c}, 8.60 \mathrm{a}$ and $8.61 \mathrm{~b}$ becomes slipindependent for a given stator current, whereas the remaining two terms on the right-hand side (RHS) of Equation 8.76a disappear if eddy currents in the rotor ring are absent. Thus, for an ideal hysteresis machine with zero eddy currents, we have
$$\frac{P_{H M}}{P_{H L}}=\frac{1-s}{s}$$
where $P_{H M}$ indicates the total mechanical power developed due to hysteresis machine action, and $P_{H L}$ indicates total hysteresis loss in the rotor of the machine. Rotor power input, $P_R$, being the sum of power loss, $P_L$ and mechanical power developed, $P_M$, we have
$$\frac{P_R}{1}=\frac{P_L}{s}=\frac{P_M}{1-s}$$
It may be noted that Equations 8.69 and 8.79 indicate that induction machines and hysteresis machines belong to the same class of machines, both satisfying Equation 8.80.

电磁学代考

物理代写|电磁学代写electromagnetism代考|Power Components

$$\begin{gathered} \mathcal{P}{H L}=(s \cdot \omega) \cdot \frac{1}{2} \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right) \ \mathcal{P}{E L}=\frac{1}{2} \cdot \frac{1}{\sigma_1} J{1 x} \cdot J_{1 x}^* \ \mathcal{P}{E M}=u_y \cdot \frac{1}{2} \alpha \cdot \mathcal{R} e\left[-e^{-j \beta} J{1 x}^* \cdot H_{1 z}\right] \ \mathcal{P}{H M}=u_y \cdot \frac{1}{2} \ell \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right) \end{gathered}$$

物理代写|电磁学代写electromagnetism代考|Slip-Power Relation

$$\frac{\mathcal{P}{H M}}{\mathcal{P}{H L}}=\frac{1-s}{s}$$

$$\mathcal{P}H=\mathcal{P}{H L}+\mathcal{P}{H M}=\frac{1}{2} \cdot \omega \cdot \alpha \cdot \sin (\beta) \cdot\left(H{1 y} \cdot H_{1 y}^+H_{1 z} \cdot H_{1 z}^\right)$$

$$\frac{P_{H M}}{P_{H L}}=\frac{1-s}{s}$$

$$\frac{P_R}{1}=\frac{P_L}{s}=\frac{P_M}{1-s}$$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PCS624

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物理代写|电磁学代写electromagnetism代考|Simplifying Assumptions

The simplifying assumptions, commonly made in such treatments, ${ }^{5-7}$ are listed below:

End effects are neglected. This results in a two-dimensional problem with no variation of fields in the axial direction.

Curvature of air-gap surfaces is neglected. Thus, no special functions are needed to express the field distributions.

Conductivity of the hysteresis ring, $\sigma_1$, is constant.

At every point in the ring, the phasor $\boldsymbol{B}$ is proportional to the phasor $\boldsymbol{H}$. The constant of proportionality is a complex number. ${ }^8$ Thus, each hysteresis loop is of elliptical shape with same slope of the axis and produces the same lag angle.
5 . For the rotor base, the conductivity, $\sigma_2$, and the permeability, $\mu_2$, are all constant.

Highly permeable stator iron $(\mu \approx \infty)$, thus fields in the stator core need not be considered.

Smooth stator air-gap surface. Stator slot opening is neglected.

A current sheet sinusoidally distributed in the peripheral direction simulates armature winding with balanced three-phase currents. This current sheet is located on the stator air-gap surface and the surface currents are in axial direction. This neglects all space harmonics in the field expressions.

The machine is connected to a balanced three-phase ac voltage supply.

Only steady-state operation is considered and displacement currents are neglected.

物理代写|电磁学代写electromagnetism代考|Field Distributions

Figure 8.4 shows an idealised machine obtained in view of the assumptions enumerated above. In this figure, $X$ represents axial, $Y$ peripheral and $Z$ radial directions. Let the stator current sheet be given as the surface current density in the axial direction:
$$K_x=K_o \cdot e^{j(\omega t-\ell y)}$$
where the amplitude of current density is $\left|K_0\right|, \omega$ is the supply frequency, $\ell=\pi / \lambda$ and $\lambda$ is the pole pitch. As shown in Figure 8.4, the permeability $(\mu)$ is assumed to have the following values:
\begin{aligned} \mu & \approx \infty \text { for the stator }(z>g) \ & =\mu_o \quad \text { for the air-gap }(g>z>0) \ & =\alpha \cdot e^{-j \beta} \quad \text { for the rotor ring }(0>z>-d) \ & =\mu_2 \quad \text { for the rotor base }(-d>z>-\infty) \end{aligned}
where $\alpha$ and $\beta$ are real positive constants. Let the rotor be moving with a velocity $u_y$ in the peripheral direction. Therefore, the slip is given by
$$s=\frac{\omega / \ell-u_y}{\omega / \ell}=1-\frac{\ell}{\omega} \cdot u_y$$
The stator current sheet, in a reference frame moving with the rotor, can be given as
$$K_x=K_o \cdot e^{j(\operatorname{sot}-\ell y)}$$
Thus, the peripheral component of the air-gap field on the stator surface can be given as
$$\left.H_{o y}\right|_{z=\mathrm{g}}=K_o \cdot e^{j(s \omega t-\ell y)}$$

电磁学代考

物理代写|电磁学代写electromagnetism代考|Simplifying Assumptions

5 .对于转子底座，电导率$\sigma_2$和磁导率$\mu_2$都是恒定的。

物理代写|电磁学代写electromagnetism代考|Field Distributions

$$K_x=K_o \cdot e^{j(\omega t-\ell y)}$$

\begin{aligned} \mu & \approx \infty \text { for the stator }(z>g) \ & =\mu_o \quad \text { for the air-gap }(g>z>0) \ & =\alpha \cdot e^{-j \beta} \quad \text { for the rotor ring }(0>z>-d) \ & =\mu_2 \quad \text { for the rotor base }(-d>z>-\infty) \end{aligned}

$$s=\frac{\omega / \ell-u_y}{\omega / \ell}=1-\frac{\ell}{\omega} \cdot u_y$$

$$K_x=K_o \cdot e^{j(\operatorname{sot}-\ell y)}$$

$$\left.H_{o y}\right|_{z=\mathrm{g}}=K_o \cdot e^{j(s \omega t-\ell y)}$$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PHYS404

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

物理代写|电磁学代写electromagnetism代考|Current Density Distribution

The current density distribution in the slot is given by the following double Fourier series:
$$J_z=\sum_{m=\text { odd }}^{\infty} \sum_{n-a d d}^{\infty} J_{m, n} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{n \pi}{2 d} \cdot y\right)$$

The Fourier coefficient $J_{m, n}$, involved in Equation 8.1, can be obtained by multiplying both sides of this equation with $\cos ((p 2 \pi / w) \ldots x) \ldots \cos ((q \pi / 2 d) \ldots y)$, and then integrating the resulting expression over $-w / 2<x<w / 2$ and $0<y<d$. Thus, on setting $p=m$ and $q=n$, we finally get
\begin{aligned} \text { LHS } & =\int_{h_1}^{h_2} \int_{-C / 2}^{c / 2}\left[\frac{I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \cos \left(\frac{p 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{q \pi}{2 d} \cdot y\right) d x \cdot d y \ & =\left[\frac{2 I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \frac{\sin ((m \pi / w) \cdot c)}{m \pi / w} \cdot \frac{\left{\sin \left((n \pi / 2 d) \cdot h_2\right)-\sin \left((n \pi / 2 d) \cdot h_2\right)\right}}{n \pi / d} \end{aligned}
where $I$ indicates the current flowing in the conductor. Note that the current density $\left[I /\left(c \cdots\left(h_2-h_1\right)\right)\right]$ is zero in the slot region beyond the conductor crosssection. Similarly,
\begin{aligned} \text { RHS } & =\sum_{m-\text { odd } n-\text { odd } d}^{\infty} \sum_{m, n} \cdot \int_{0-w / 2}^d \int^{w / 2} \cos \left(\frac{m \pi \cdot x}{w / 2}\right) \cdot \cos \left(\frac{n \pi \cdot y}{2 d}\right) \cdot \cos \left(\frac{p \pi \cdot x}{w / 2}\right) \cdot \cos \left(\frac{q \pi \cdot y}{2 d}\right) \ & =\frac{d \cdot w}{4} \cdot J_{m, n} \end{aligned}
Thus, we finally get the current density distribution by the following expression:
$$J_{m, n}=\left[\frac{8 I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \frac{\sin ((m \pi / w) \cdot c)}{m \pi} \cdot \frac{\left{\sin \left((n \pi / 2 d) \cdot h_2\right)-\sin \left((n \pi / 2 d) \cdot h_2\right)\right}}{n \pi}$$

物理代写|电磁学代写electromagnetism代考|Vector Magnetic Potentia

Once the current density distribution is known, the vector magnetic potential in the slot region can be obtained from the relation
$$\nabla^2 A_z=-\mu_o J_z$$
The distribution of vector magnetic potential $\left(A_z\right)$ in the slot consists of two parts. These include the particular integral $\left(A_{z 1}\right)$ and the complementary function $\left(A_{z 2}\right)$. The expression for $A_{z 1}$ is an even function of $x$. Thus, in view of Equation 8.1, $A_{z 1}$ can be expressed as
$$A_{z 1}=\sum_{m-\text { odd } n-\text { add }}^{\infty} \sum_{m, n}^{\infty} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{n \pi}{2 d} \cdot y\right)$$
The coefficient $A_{m, n}$ can be determined by substituting this expression in Equation 8.5. Thus, in view of Equation 8.1, we get
$$A_{m, n}=J_{m, n} \cdot \frac{\mu_o}{\left[(m 2 \pi / w)^2+(n \pi / 2 d)^2\right]}$$
The complementary function $A_{z 2}$ that describes the potential distribution in the open rectangular slot can be determined in view of the flux density distribution.

电磁学代考

物理代写|电磁学代写electromagnetism代考|Current Density Distribution

$$J_z=\sum_{m=\text { odd }}^{\infty} \sum_{n-a d d}^{\infty} J_{m, n} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{n \pi}{2 d} \cdot y\right)$$

\begin{aligned} \text { LHS } & =\int_{h_1}^{h_2} \int_{-C / 2}^{c / 2}\left[\frac{I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \cos \left(\frac{p 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{q \pi}{2 d} \cdot y\right) d x \cdot d y \ & =\left[\frac{2 I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \frac{\sin ((m \pi / w) \cdot c)}{m \pi / w} \cdot \frac{\left{\sin \left((n \pi / 2 d) \cdot h_2\right)-\sin \left((n \pi / 2 d) \cdot h_2\right)\right}}{n \pi / d} \end{aligned}

\begin{aligned} \text { RHS } & =\sum_{m-\text { odd } n-\text { odd } d}^{\infty} \sum_{m, n} \cdot \int_{0-w / 2}^d \int^{w / 2} \cos \left(\frac{m \pi \cdot x}{w / 2}\right) \cdot \cos \left(\frac{n \pi \cdot y}{2 d}\right) \cdot \cos \left(\frac{p \pi \cdot x}{w / 2}\right) \cdot \cos \left(\frac{q \pi \cdot y}{2 d}\right) \ & =\frac{d \cdot w}{4} \cdot J_{m, n} \end{aligned}

$$J_{m, n}=\left[\frac{8 I}{c \cdot\left(h_2-h_1\right)}\right] \cdot \frac{\sin ((m \pi / w) \cdot c)}{m \pi} \cdot \frac{\left{\sin \left((n \pi / 2 d) \cdot h_2\right)-\sin \left((n \pi / 2 d) \cdot h_2\right)\right}}{n \pi}$$

物理代写|电磁学代写electromagnetism代考|Vector Magnetic Potentia

$$\nabla^2 A_z=-\mu_o J_z$$

$$A_{z 1}=\sum_{m-\text { odd } n-\text { add }}^{\infty} \sum_{m, n}^{\infty} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot x\right) \cdot \cos \left(\frac{n \pi}{2 d} \cdot y\right)$$

$$A_{m, n}=J_{m, n} \cdot \frac{\mu_o}{\left[(m 2 \pi / w)^2+(n \pi / 2 d)^2\right]}$$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

物理代写|电磁学代写electromagnetism代考|PHYS415

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物理代写|电磁学代写electromagnetism代考|Field Distribution in Stator Slots

In view of the above description, we can now write the field expression in terms of vector magnetic potential and the magnetic field intensity in the region related to the stator slots.
Vector Magnetic Potential
With reference to Figure 7.4, the distribution of vector magnetic potential in the current-carrying stator slot can be expressed as a real part of a complex expression, as given below.

\begin{aligned} A_{s x}^o= & \mathcal{R} e\left[\sum_{m-\text { odd }}^{\infty} \sum_{n-\text { odd }}^{\infty} A_{m, n} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \cdot \cos {(n \pi / 2 d) \cdot(z+g+d)}\right. \ & +\sum_{p-\text { odd }}^{\infty} a_p^o \cdot\left(\frac{w}{p 2 \pi}\right) \cdot \cos \left(\frac{p 2 \pi}{w} \cdot y\right) \cdot \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \ & \left.+\sum_{q-\text { odd }}^{\infty} b_q^o \cdot\left(\frac{w}{q \pi}\right) \cdot \sin \left(\frac{q \pi}{w} \cdot y\right) \cdot \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)}\right] \cdot e^{j \omega t} \end{aligned}
where $A_{m, n}$ is given by Equation 8.7 in Chapter 8 . Further, $a_p^o$ and $b_q^o$ indicate two sets of complex arbitrary constants.

For the $r$ th current-free slot, the distribution of vector magnetic potential can now be expressed as
\begin{aligned} A_{s x}^r= & \operatorname{Re} e\left[\sum_{p-\text { odd }}^{\infty} a_p^r \cdot\left(\frac{w}{p 2 \pi}\right) \cdot \cos \left{\frac{p 2 \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)}\right. \ & \left.+\sum_{q-\text { odd }}^{\infty} b_q^r \cdot\left(\frac{w}{q \pi}\right) \cdot \sin \left{\frac{q \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)}\right] \cdot e^{j \omega t} \end{aligned}
over $(r \lambda-w / 2)<y<(r \lambda+w / 2)$, for $r=1,2, \ldots,(3 \eta-1)$, where $a_p^r$ and $b_q^r$ indicate two sets of complex arbitrary constants, for value of each $r$.

物理代写|电磁学代写electromagnetism代考|Magnetic Field Intensity

The components of the magnetic field intensity in stator slots obtained in view of Equations 7.1 and 7.2 are as follows:
\begin{aligned} H_{s y}^o= & \frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^o}{\partial z} \ = & -\mathcal{R} e \sum_{m-\text { oddd }}^{\infty} \sum_{n-a d d}^{\infty} \frac{A_{m, n}}{\mu_o} \cdot \frac{n \pi}{2 d} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \cdot \sin \left{\frac{n \pi}{2 d} \cdot(z+g+d)\right} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{p-o d d}^{\infty} \frac{a_p^o}{\mu_o} \cdot \cos \left(\frac{p 2 \pi}{w} \cdot y\right) \cdot \frac{\sinh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & +\operatorname{Re} e \sum_{q-o d d}^{\infty} \frac{b_q^o}{\mu_o} \cdot \sin \left(\frac{q \pi}{w} \cdot y\right) \cdot \frac{\sinh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}

over $(-w / 2)<y<(+w / 2)$,
\begin{aligned} H_{s z}^o= & -\frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^o}{\partial y} \ = & -\mathcal{R} e \sum_{m-\text { odd }}^{\infty} \sum_{n-\text { odd }}^{\infty} \frac{A_{m, n}}{\mu_o} \cdot \frac{n \pi}{2 d} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \ & \times \sin \left{\frac{n \pi}{2 d} \cdot(z+g+d)\right} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{p-\text { odd }}^{\infty} \frac{a_p^o}{\mu_o} \cdot \sin \left(\frac{p 2 \pi}{w} \cdot y\right) \ & \times \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & -\operatorname{Re} \sum_{q-\text { odd }}^{\infty} \frac{b_q^o}{\mu_o} \cdot \cos \left(\frac{q \pi}{w} \cdot y\right) \ & \times \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}
over $(-w / 2)<y<(+w / 2)$,
\begin{aligned} H_{s y}^r= & \frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^r}{\partial z}=\mathcal{R} e \sum_{p-o d d}^{\infty} \frac{a_p^r}{\mu_o} \cdot \cos \left{\frac{p 2 \pi}{w} \cdot(y-r \lambda)\right} \ & \times \frac{\sinh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{q-\text { odd }}^{\infty} \frac{b_q^r}{\mu_o} \cdot \sin \left{\frac{q \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\sinh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}

电磁学代考

物理代写|电磁学代写electromagnetism代考|Field Distribution in Stator Slots

\begin{aligned} A_{s x}^o= & \mathcal{R} e\left[\sum_{m-\text { odd }}^{\infty} \sum_{n-\text { odd }}^{\infty} A_{m, n} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \cdot \cos {(n \pi / 2 d) \cdot(z+g+d)}\right. \ & +\sum_{p-\text { odd }}^{\infty} a_p^o \cdot\left(\frac{w}{p 2 \pi}\right) \cdot \cos \left(\frac{p 2 \pi}{w} \cdot y\right) \cdot \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \ & \left.+\sum_{q-\text { odd }}^{\infty} b_q^o \cdot\left(\frac{w}{q \pi}\right) \cdot \sin \left(\frac{q \pi}{w} \cdot y\right) \cdot \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)}\right] \cdot e^{j \omega t} \end{aligned}

\begin{aligned} A_{s x}^r= & \operatorname{Re} e\left[\sum_{p-\text { odd }}^{\infty} a_p^r \cdot\left(\frac{w}{p 2 \pi}\right) \cdot \cos \left{\frac{p 2 \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)}\right. \ & \left.+\sum_{q-\text { odd }}^{\infty} b_q^r \cdot\left(\frac{w}{q \pi}\right) \cdot \sin \left{\frac{q \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)}\right] \cdot e^{j \omega t} \end{aligned}

物理代写|电磁学代写electromagnetism代考|Magnetic Field Intensity

\begin{aligned} H_{s y}^o= & \frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^o}{\partial z} \ = & -\mathcal{R} e \sum_{m-\text { oddd }}^{\infty} \sum_{n-a d d}^{\infty} \frac{A_{m, n}}{\mu_o} \cdot \frac{n \pi}{2 d} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \cdot \sin \left{\frac{n \pi}{2 d} \cdot(z+g+d)\right} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{p-o d d}^{\infty} \frac{a_p^o}{\mu_o} \cdot \cos \left(\frac{p 2 \pi}{w} \cdot y\right) \cdot \frac{\sinh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & +\operatorname{Re} e \sum_{q-o d d}^{\infty} \frac{b_q^o}{\mu_o} \cdot \sin \left(\frac{q \pi}{w} \cdot y\right) \cdot \frac{\sinh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}

\begin{aligned} H_{s z}^o= & -\frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^o}{\partial y} \ = & -\mathcal{R} e \sum_{m-\text { odd }}^{\infty} \sum_{n-\text { odd }}^{\infty} \frac{A_{m, n}}{\mu_o} \cdot \frac{n \pi}{2 d} \cdot \cos \left(\frac{m 2 \pi}{w} \cdot y\right) \ & \times \sin \left{\frac{n \pi}{2 d} \cdot(z+g+d)\right} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{p-\text { odd }}^{\infty} \frac{a_p^o}{\mu_o} \cdot \sin \left(\frac{p 2 \pi}{w} \cdot y\right) \ & \times \frac{\cosh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & -\operatorname{Re} \sum_{q-\text { odd }}^{\infty} \frac{b_q^o}{\mu_o} \cdot \cos \left(\frac{q \pi}{w} \cdot y\right) \ & \times \frac{\cosh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}

\begin{aligned} H_{s y}^r= & \frac{1}{\mu_o} \cdot \frac{\partial A_{s x}^r}{\partial z}=\mathcal{R} e \sum_{p-o d d}^{\infty} \frac{a_p^r}{\mu_o} \cdot \cos \left{\frac{p 2 \pi}{w} \cdot(y-r \lambda)\right} \ & \times \frac{\sinh {(p 2 \pi / w) \cdot(z+g+d)}}{\cosh ((p 2 \pi / w) \cdot d)} \cdot e^{j \omega t} \ & +\mathcal{R} e \sum_{q-\text { odd }}^{\infty} \frac{b_q^r}{\mu_o} \cdot \sin \left{\frac{q \pi}{w} \cdot(y-r \lambda)\right} \cdot \frac{\sinh {(q \pi / w) \cdot(z+g+d)}}{\cosh ((q \pi / w) \cdot d)} \cdot e^{j \omega t} \end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。