Mathematic的函数作图总结
一、 Mathematic做图总结：
随着数学的计算技术不断地发展，出现了许多优秀的数学软件。使用这些数学软件，可以大大地提高我们分析和解决数学问题的能力。数学软件Mathematica功能比较强大，它集数值计算、公式推导和图形等功能为一体。可以顺利解决我们在高等数学、线性代数、概率论、最优化、概率统计等一些数学科目中所要经常遇到的一些问题。
Mathematica在操作是必须得注意大小写，内部函数一般要写全称，而且一定是以大写英文字母开头，自定义的变量可以取任意的名称，长度不限但是不可以以数字开头，（）用来表示项的结合顺序，而[]表示函数。
Mathematica的图形函数十分丰富，用它可以画出很复杂的图形，而且只需要寥寥几句就可以，具有十分方便的操作性能。Mathematica可以用来函数的各类函数画图：例如所有的三角函数，反三角函数，以及各类的特殊函数，各种的复杂函数各种的随机函数等等图形的输出。函数的各种表示方法（列表法，解析法(直角坐标方程，参数方程，极坐标方程，隐函数)）
Mathematic做图分为二维的和三维的
二、 根据函数维数对Mathematic做图作总结：
二维图形：
例如：
![](https://wkrtcs.bdimg.com/rtcs/image?w=270&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"270","h":"21","dataType":"png","c":"word/media/image1_1.png","imgOriW":229,"imgOriH":18})
![](https://wkrtcs.bdimg.com/rtcs/image?w=364&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"364","h":"222","dataType":"png","c":"word/media/image2_1.png","imgOriW":288,"imgOriH":177})
例如：用ImplicitPlot命令作出![](https://wkrtcs.bdimg.com/rtcs/image?w=101&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"101","h":"24","dataType":"gif","c":"word/media/image3.png"})
的图形
![](https://wkrtcs.bdimg.com/rtcs/image?w=361&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"361","h":"361","dataType":"png","c":"word/media/image4_1.png","imgOriW":288,"imgOriH":288})
再例如：
用不同颜色画出![](https://wkrtcs.bdimg.com/rtcs/image?w=209&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"209","h":"21","dataType":"gif","c":"word/media/image5.png"})
的图形，并写出命令。
![](https://wkrtcs.bdimg.com/rtcs/image?w=528&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"528","h":"109","dataType":"png","c":"word/media/image6_1.png","imgOriW":396,"imgOriH":82})
![](https://wkrtcs.bdimg.com/rtcs/image?w=361&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"361","h":"222","dataType":"png","c":"word/media/image7_1.png","imgOriW":288,"imgOriH":177})
由图可以看出 Mathematic可以在一幅图中用多种颜色表示图像图像更清晰明了。即颜色函数RGBColor[red,green,blue]
用PolarPlot命令, 作出曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=79&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"79","h":"21","dataType":"gif","c":"word/media/image8.png"})
（极坐标表示）的图形。
![](https://wkrtcs.bdimg.com/rtcs/image?w=270&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"270","h":"45","dataType":"png","c":"word/media/image9_1.png","imgOriW":229,"imgOriH":38})
![](https://wkrtcs.bdimg.com/rtcs/image?w=339&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"339","h":"339","dataType":"png","c":"word/media/image10_1.png","imgOriW":287,"imgOriH":287})
由图可知我们可以运用软件通过简简单单的语言设计一个复杂的图形
三维图形：
Mathematica可以绘制三维图形,例如: In[1]:=Plot3D[Sin[x*y],{x,0,Pi},{y,0,Pi}]绘制一幅z=sin(xy)的图形.
ParametricPlot[{fx,fy},{t,tmin,tmax}] 平面曲线的参数图
ParametricPlot3D[{fx,fy,fz},{t,tmin,tmax}] 空间曲线的参数图
ParametricPlot3D[{fx,fy,fz},{t,tmin,tmax},{u,umin,umax}] 空间曲面的参数图
例如：画出球面![](https://wkrtcs.bdimg.com/rtcs/image?w=103&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"103","h":"24","dataType":"gif","c":"word/media/image11.png"})
。
![](https://wkrtcs.bdimg.com/rtcs/image?w=650&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"650","h":"25","dataType":"png","c":"word/media/image12_1.png","imgOriW":625,"imgOriH":21})
![](https://wkrtcs.bdimg.com/rtcs/image?w=311&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"311","h":"339","dataType":"png","c":"word/media/image13_1.png","imgOriW":263,"imgOriH":287})
还可以画出另一些三维图形 例如：
![](https://wkrtcs.bdimg.com/rtcs/image?w=400&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"400","h":"212","dataType":"png","c":"word/media/image14.png","imgOriW":300,"imgOriH":225})
![](https://wkrtcs.bdimg.com/rtcs/image?w=311&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"311","h":"275","dataType":"png","c":"word/media/image15.png","imgOriW":300,"imgOriH":265})
双叶双曲面图形
![](https://wkrtcs.bdimg.com/rtcs/image?w=442&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"442","h":"42","dataType":"png","c":"word/media/image16_1.png","imgOriW":399,"imgOriH":38})
![](https://wkrtcs.bdimg.com/rtcs/image?w=217&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"217","h":"235","dataType":"png","c":"word/media/image17_1.png","imgOriW":265,"imgOriH":287})
马鞍面：
![](https://wkrtcs.bdimg.com/rtcs/image?w=337&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"337","h":"273","dataType":"png","c":"word/media/image18_1.png","imgOriW":265,"imgOriH":287})
等等
我们还可以自己画出一些有意思的图形
![](https://wkrtcs.bdimg.com/rtcs/image?w=480&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"480","h":"184","dataType":"png","c":"word/media/image19_1.png","imgOriW":360,"imgOriH":138})
![](https://wkrtcs.bdimg.com/rtcs/image?w=428&md5sum=305013067b9fd9822eef03e0fb27fe13&sign=6a05ac21a1&rtcs_flag=1&rtcs_ver=3.3&l=webapp&bucketNum=12&ipr={"t":"img","w":"428","h":"470","dataType":"png","c":"word/media/image20_1.png","imgOriW":132,"imgOriH":145})
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