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# 数学代写|微积分代写Calculus代考|Math222 A Few Preliminaries

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## 数学代写|微积分代写Calculus代考|A Few Preliminaries

Here is what’s ahead: this first chapter is a review, which will be useful later on; Chapter 2 is on differential calculus; and Chapter 3 introduces integral calculus. Chapter 4 presents some more advanced topics. At the end of each chapter there is a summary to help you review the material in that chapter. There are two appendixes – one gives proofs of a number of relations used in the book, and the other describes some supplementary topics. In addition, there is a list of extra problems with answers in the Review Problems on page 277, and a section of tables you may find useful.

First we review the definition of a function. If you are already familiar with this and with the idea of dependent and independent variables, skip to frame 14. (In fact, in this chapter there is ample opportunity for skipping if you already know the material. On the other hand, some of the material may be new to you, and a little time spent on review can be a good thing.)

A word of caution about the next few frames. Because we start with some definitions, the first section must be somewhat more formal than most other parts of the book.

## 数学代写|微积分代写Calculus代考|Functions

The definition of a function makes use of the idea of a set. If you know what a set is, go to 4. If not, read on.

A set is a collection of objects – not necessarily material objects-described in such a way that we have no doubt as to whether a particular object does or does not belong to it. A set may be described by listing its elements. Example: 23, 7, 5, 10 is a set of numbers. Another example: Reykjavik, Ottawa, and Rome is a set of capitals.

We can also describe a set by a rule, such as all the even positive integers (this set contains an infinite number of objects).

A particularly useful set is the set of all real numbers. This includes all numbers such as $5,-4,0,1 / 2, \pi,-3.482, \sqrt{2}$. The set of real numbers does not include quantities involving the square root of negative numbers. Such quantities are called complex numbers; in this book we will be concerned only with real numbers.

The mathematical use of the word “set” is similar to the use of the same word in ordinary conversation, as “a set of chess pieces.”

Now we are ready to talk about functions. Here is the definition.
A function is a rule that assigns to each element in a set $A$ one and only one element in a set $B$.

The rule can be specified by a mathematical formula such as $y=x^2$, or by tables of associated numbers, for instance, the temperature at each hour of the day. If $x$ is one of the elements in set $A$, then the element in set $B$ that the function $f$ associates with $x$ is denoted by the symbol $f(x)$. This symbol $f(x)$ is the value of $f$ evaluated at the element $x$. It is usually read as ” $f$ of $x$.”
The set $A$ is called the domain of the function. The set of all possible values of $f(x)$ as $x$ varies over the domain is called the range of the function. The range of $f$ need not be all of $B$.

## 数学代写|微积分代写Calculus代考|Functions

“set”这个词在数学上的用法类似于普通对话中同一个词的用法，如“一组棋子”。

## 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。