Mathematica入门学习

Mathematica 介绍

introduction to Mathematica

 

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今天小编为大家带来的主题是mathematica，

欢迎您的用心访问。

本期推文阅读时常大约5分钟，

请您耐心阅读。

 

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Dear, here is Learingyard Academy!

 

Today, Xiaobian is Mathematica, which is Mathematica.

 

Welcome your intention to access.

 

It is often about 5 minutes from this period.

 

Please read patiently.

 

萌说新语——Mathematica入门学习音频：00:00/02:02

 

#01

 

本期主题介绍

The topic of this issue

 

您是否还在为科研论文上复杂的计算而烦恼？

您是否动笔计算计算到凌晨3点？

别担心，

本期推文将帮助你解决科研计算上的烦恼！

上手Mathematica,您就可以远离计算烦恼！

所以，

请感兴趣的小伙伴和小编一起开启，

学习Mathematica的旅程吧！

Are you still worrying about complex calculations on scientific research papers?

Did you start the calculation until 3 o'clock in the morning?

do not worry,

This tweet will help you solve some of the troubles in scientific research and calculation!

This tweet will help you solve your problems in scientific research calculations!

so,

Please start with interested friends and editors,

Learn the journey of Mathematica!

 

#02

 

Mathematica软件介绍

Matlab software introduction

Mathematica是一款科学计算软件，很好地结合了数值和符号计算引擎、图形系统、编程语言、文本系统、和与其他应用程序的高级连接。

Mathematica的功能也非常强大，原生函数非常多，有近5000个，并涉及多个领域。小编在此针对入门级简单操作进行介绍！

 

Mathematica is a scientific computing software that combines numerical and symbolic computing engines, graphics systems, programming languages, text systems, and advanced connections with other applications.

Mathematica is also very powerful. There are many native functions, nearly 5,000, and involve multiple fields. The editor here introduces the entry-level simple operation!

#03

Mathematica基础介绍

Basic introduction to Mathematica

 

1.Mathematica如何运行？

1.How does Mathematica work?

无论是下载软件还是在网页上操作Wolfram笔记本，只需要直接输入表达式，然后用键盘上的“shift+enter"键就可以运行了。

Whether you are downloading software or operating a Wolfram notebook on a web page, you only need to directly enter the expression, and then use the "shift+enter" key on the keyboard to run it.

 

2.函数与变量

要想学会计算，首先得学会函数与变量怎么定义与命名。

1）Mathematica中，变量名可以以字母开头和数字组成，最好是小写字母开头，这样可以便于与Mathematica中的内置函数区分。

2)两个变量之间添加空格或者数字会默认为乘法运算。

3）自定义函数结构：使用“f[x_]:=”。注意要有“：”。

那么 “ = ”与“ ：=”有什么区别呢？我们通过下列计算来分析

 

2.Functions and variables

1）To learn to calculate, you must first learn how to define and name functions and variables

2）In Mathematica, variable names can start with a letter and a number, preferably a lowercase letter, which can be easily distinguished from the built-in functions in Mathematica.

3）Adding spaces or numbers between two variables will default to multiplication.

Custom function structure: use "f[x_]:=". Pay attention to ":".

So what is the difference between "=" and ":="? We use the following calculations to analyze

 

在应用“=”的时候，我们可以看到，如果变量已经被赋值，那么 会直接将变量的 值带入 函数事计算，所以，自定义函数时，应当尽量用”：=“。

 

When applying "=", we can see that if the variable has been assigned, then the value of the variable will be directly brought into the function calculation. Therefore, when customizing the function, you should try to use ":=".

 

#04

函数求导与求积分

Function derivation and integration

1.Mathematica求导格式：

1. Mathematica derivation format:

D[f,x] 表示f对x求一阶导数

D[f,{x，n}] 表示f对x求n阶导数

举例：

 

For example:

D[f,x] means the first derivative of f with respect to x

D[f,{x,n}] means that f finds the n-th order derivative of x

 

2.函数求积分

2. Integrate function

求积分的命令用Integrate或者输入传统的积分符号求积分。

函数名[变量名_]:=函数：

Integrate[函数名[变量名],变量名]

Use Integrate or enter the traditional integral symbol to find the integral.

Function name[variable name_]:=function:

Integrate[functionname[variablename],variable name]

 

线积分

Line integral

Integrate[求积函数，{变量范围}]

Integrate[Integration function, {variable range}]

二重积分

Double integral

Integrate[求积函数，{变量范围}，{变量范围}]

注：函数用[ ],变量范围用大括号{ }

Integrate[Integration function, {variable range}, {variable range}]

Note: Use [] for functions and curly braces {} for variable ranges

 

如果遇到特殊符号的输入，可以通过Mathematica菜单栏上的面板工具——数学助手寻求帮助。

If you encounter the input of special symbols, you can ask for help through the panel tool-Math Assistant on the Mathematica menu bar.

 

#05

运用Plot绘图

 

1.Plot二维绘图:

Plot two-dimensional drawing:

Mathematic中的可视化基础绘图用plot函数，可以用于点、线等绘图。

Plot函数格式：Plot[函数的解析式，{自变量，范围}]

举例：绘制一个正弦函数图像

 

The Plot function for visual basic drawing in Mathematic can be used for drawing points, lines etc.

Format of Plot function: Plot[analytic expression of function, {argument, range}]

Example: draw a graph of sine function

 

Mathematica还提供很多有用的定制化图像，如图通过“PlotLegends”添加图例。

 

Mathematica also provides a lot of useful customized images, as shown in the figure, add a legend through "PlotLegends"

 

2.Plot3D绘图

Plot3D drawing

Mathematica还提供Plot3D绘图函数，其函数格式为：Plot3D[函数，{变量范围}]

若想要吧多个函数放到同一张图，可以用大括号括函数，其函数格式为Plot3D[{函数1，函数2}，{变量范围}]

 

Mathematica also provides Plot3D drawing function, the function format is: Plot3D[function, {variable range}]

If you want to put multiple functions in the same picture, you can use curly braces to enclose the function, the function format is Plot3D[{function 1, function 2}, {variable range}]

 

举例：我们画一个函数的三维图形

 

Example: we draw a three-dimensional graph of a function

 

举例:我们画两个函数的三维图形

 

Example:we draw three-dimensional graphics of two functions

 

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