﻿ ﻿﻿﻿ Fractional Calculus Computer Algebra System math software + + =  ﻿

# Example of Math Function Graphics 数学函数图 制图法

A simple straightforward way to run interactive mathematics in a web page is by mathHand.com. Some examples come from Paul Masson (refer to Reference).

In order to plot complex function, you should convert it to complex by tocomplex(x) before plot. Use complex(x) to set variable for complex variable in real value, and Use complex(0,x) to set variable for complex variable in imag value. Get real part by re() and imag part by im(). e.g. convert log(x) to re(log(complex(x))).

## plot 制图

plot(x), implicitplot(x=y), parametricplot(t,t), tangentplot(x), secantplot(x), polarplot(x), overlapplot(x)

The plot( ) function plots a function, implicit function, parametric function, polar.

Here are some particularly nice curve examples by plot function plot( )

### Animation

The plot( ) plots animation by adding the timer(x) into your formula.

## plot3DIE 制图3DIE

The plot3DIE( ) plots a function, parametric function in 3D graph.

Here are some particularly nice examples by plot function plot3DIE( )

plot3DIE(x*y), 立体图IE,

### Animation

• bianchi-pinkall-animation
• bianchi-pinkall-animation zoomed

The following plot functions did not work on Microsoft IE and QQ browsers. Please use Google Chrome browser.

plot3D(x*y), contour3D(x*y), wireframe3D(x*y), implicit3D(x*y*z), complex3D(x), parametric3D(t,t,t), parametric3Dxy(x,y,x*y), wireframe3Dxy(x,y,x*y), spin3D(x)
立体图, 立体外形图, 立体线框图, 立体隐函数图, 复数图, 立体参数图t, 立体参数图xy, 立体线框图xy, 旋转图3D

Notice that Microsoft Internet Explorer IE did not support svg, so IE cannot show following graph, please use other browrer.

## plot2D 制图2D

The plot2D( ) plots a list of data, function, implicit function, parametric function, piecewise function, polar plot, derivative, integral by a differential equation dy/dx=f(x,y) graphically. e.g. integral of cos(x) :
dy/dx = cos(x)

### solve dy/dx=f(x,y) graphically

Some differential equations cannot be solved symbolly, but can be solved graphically by a plot function plot2D( ), or click the plot2D button. e.g.
dy/dx = sin(x)-cos(y)

Here are some particularly nice examples by plot function plot2D( )

Bessel function of the first kind besselJ( n, x ) — the first five Bessel function of the first kind of real or complex order n of a real or complex number.

Bessel functions of the first or second kind for both positive (blue) and negative (red) real order, and derivative.

Cornu Spiral - the Fresnel cosine and sine integrals.

### Animation

The plot2D( ) plots animation by clicking the animate checkbox and/or adding the timer(x) into your formula.
• choreographies
• butterfly
• square
• Unwrapping Circle
• Weierstrass

## plot3D 制图3D

The plot3D( ) plots a function, implicit function, parametric function in 3D graph. The figure can be rotated by clicking and dragging with a mouse or swiping on a touch device, as well as zoomed in or out with a mouse wheel or pinching on a touch device.

Here are some particularly nice examples by plot function plot3D( )

Schwarz Primitive Surface cos(x)+cos(y)+cos(z) = 0

### Animation

It plots animation by clicking the spin checkbox.

## complex3D 复变函数图3D

The complex3D( ) plots a function on the complex plane and space.

Here are some particularly nice examples by plot function complex3D( ) that show real and imaginary parts of complex function including special functions on complex axes and plane.

## spin3D 旋转图3D

The spin3D( ) plots spin of a function, implicit function, parametric function, a spacial curve, and its inverse in 3D graph.

1. a plane in space. 2. a curve in space. 3. cross-section. 4. positive value of a curve spins to make stereo.

• x^2+y^2=1

## implicit3D 隐函数图3D

The implicit3D( ) can plot a 4-dimensional (x,y,z,t) object in 3D space. You manually change the t value by slider. e.g.
• x*x-y*y-z*z-t-1

### Animation

It plots animation by clicking the spin checkbox.

## Reference 参阅

• example 例题
• graph 制图
• graphics 制图法
• animation 动画 ﻿