• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 商科代写|商业数学代写business mathematics代考|SUMMARY OF KEY POINTS

Key Terms

• Degree of a polynomial
• Domain
• Euler’s number, e
• Exponential function
• First-degree polynomial function
• Function
• Linear function
• Polynomial function
• Power function
• Rational function
• Second-degree polynomial function
• Zero function
Key Concepts
Functions
• A function consists of two sets and an assignment rule between them, which assigns every value in the first set a unique, but not necessarily different, element of the second set.
• Functions can be specified by words, equation, graphs, or tables.
• When a graph depicts a function, the domain is always placed on the horizontal axis and the range on the vertical axis. The assignment rule assigns a number on the vertical axis to each value on the horizontal axis.
• A graph represents a function if and only if the graph passes the vertical line test. This test requires that any and all vertical lines that cross the horizontal axis at a value in the domain must intersect the graph at one and only one point.

The solutions to equations of the form $a x^{2}+b x+c=0$ are given by the quadratic formula ${ }^{4}$
$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$
To solve any quadratic equation, substitute the values of its coefficients $a$, $b$, and $c$ into the quadratic formula and simplify.
Example 1 Solve the equation $x^{2}+2 x-3=0$ for $x$.
Solution This is a quadratic equation with $a=1, b=2$, and $c=-3$. Substituting these values into the quadratic formula, we obtain
$$x=\frac{-2 \pm \sqrt{2^{2}-4(1)(-3)}}{2(1)}=\frac{-2 \pm \sqrt{4+12}}{2}=\frac{-2 \pm \sqrt{16}}{2}=\frac{-2 \pm 4}{2}$$
Using the plus sign, we obtain one solution as $x=(-2+4) / 2=1$. Using the minus sign, we find a second solution as $x=(-2-4) / 2=-3$.

Example 2 Solve the equation $4 y^{2}-2 y=3$ for $y$.
Solution We first rewrite this equation in the form as $4 y^{2}-2 y-3=0$, which is a quadratic equation with $a=4, b=-2$, and $c=-3$. Substituting these values into the quadratic formula, we have
$$y=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(4)(-3)}}{2(4)}=\frac{2 \pm \sqrt{4+48}}{8}=\frac{-2 \pm \sqrt{52}}{8}=\frac{2 \pm 7.21}{8}$$
The solutions are then $y=(2+7.21) / 8=1.15$ and $y=(2-7.21) / 8=-0.65$, with all calculations rounded to two decimals.

The quadratic formula does not always yield two solutions. If $b^{2}-4 a c=0$, the formula reduces to
$$x=\frac{-b \pm \sqrt{0}}{2 a}=-\frac{b}{2 a}$$
In these cases, the quadratic equation has only one solution. If $b^{2}-4 a c$ is negative, the square root cannot be taken, and no real solutions exist. Readers familiar with complex numbers will note that this case has complex solutions. Because complex numbers have no use in commercial situations, we do not consider them here.

Individuals organizations, businesses, and countries exchange their goods and services for the products of others. Bartering was one of the earliest means of establishing trade – a farmer and a weaver might exchange one bushel of corn for one wool scarf – but bartering soon gave way to currency, first in silver and gold coins and more recently script (paper money), as the primary unit of trade. Script itself has little intrinsic worth; the real value of money is its acceptance as a recognized unit of trade, just as bitcoin is being similarly recognized. With money as a medium, a bushel of corn worth $\$ 10$and a wool scarf worth$\$13$ can be traded fairly, generally through a succession of wholesalers and distributors.

Money can either be saved, borrowed, and lent. Money is saved to buy consumer goods, such as television sets and iPhones; it is borrowed to finance purchases such as homes, cars, and college educations, and it is lent by banks and other financial institutions to make these purchases. Each dollar, pound, mark, shilling, yen, rubble, or peso that is lent or borrowed exact a charge or cost called interest.

The amount of money lent or borrowed is called the principal, usually denoted as $\boldsymbol{P}$, and the duration of the loan is its maturity, denoted as $\boldsymbol{t}$. In the simplest type of interest computation, the interest payment is directly proportional to the product of the principal and maturity. The constant of proportionality is the interest rate, denoted as $r$.

If we let $\boldsymbol{I}$ denoted the total interest, $\boldsymbol{t}$ the duration of the loan, and write $\boldsymbol{r}$ as a decimal value in terms of the same unit of time as $t$, then
$$I=\boldsymbol{P} t$$
Equation $4.1$ is the simple interest formula.

## 商科代写|商业数学代写business mathematics代考|SUMMARY OF KEY POINTS

• 多项式的次数
• 领域
• 欧拉数，e
• 指数函数
• 一阶多项式函数
• 功能
• 线性函数
• 多项式函数
• 电源功能
• 二次公式
• 二次函数
• 有理函数
• 二阶多项式函数
• 零功能
关键概念
功能
• 一个函数由两个集合和它们之间的分配规则组成，它将第一个集合中的每个值分配给第二个集合的唯一但不一定不同的元素。
• 函数可以用文字、方程式、图形或表格来指定。
• 当图形描述一个函数时，域总是放在水平轴上，而范围放在垂直轴上。分配规则将垂直轴上的数字分配给水平轴上的每个值。
• 当且仅当图形通过垂直线测试时，图形才表示函数。此测试要求在域中的某个值处与水平轴相交的任何和所有垂直线必须在一个且仅一个点与图形相交。

X=−b±b2−4一个C2一个

X=−2±22−4(1)(−3)2(1)=−2±4+122=−2±162=−2±42

X=−b±02一个=−b2一个

## 有限元方法代写

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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。