﻿﻿﻿ math handbook calculator - Fractional Calculus Computer Algebra System software + + + = ﻿

# Example of Graphics

## Real function

### in real domain

Input your function, click the plot button. e.g.
1. pow(x,x)

### in Laplace domain

First graph is in real domain, second graph is in Laplace domain by Lapalce transform laplace(x)
Input your function, click the laplace button. e.g.
2. laplace(sin(x))

### in Fourier domain

First graph is in real domain, second graph is in Fourier domain by Fourier transform fourier(x)
Input your function, click the Fourier button. e.g.
3. fourier(exp(x))
4. sine wave
5. Weierstrass function animation

### in convolution domain

First graph is in real domain, second graph is in convolution domain by convolution transform convolute(x) with x
Input your function, click the convolute button. e.g.
6. convolute(exp(x))

### in contour domain

put your function f(x,y) into sin(f(x,y)) by contour transform sin(z). First graph is in real domain, second graph is in contour domain.
Input your function, click the plot button. e.g.
7. sin(x*x+y*y-1)
Input your function, click the plot2D button. e.g.
8. plot2D( sin(x*x+y*y-1) )

### in polar domain

Input your function, click the polar button. e.g.
9. polarplot(1)

by parametricplot( )

10. parametricplot(cos(x),sin(x))
11. parametric3D(cos(x),sin(x))

### in 3D polar domain

by parametric3D, e.g.
12. parametric3D(x)
13. parametric3D(cos(x),sin(x),x)

by wireframe3D. e.g.

14. wireframe3D(x)
15. wireframe3D(cos(x),sin(x),x)

More is in graph.

## Complex function

### in real domain

First graph is real function, second graph is complex function, where blue line is real part re(z) and red line is imag part im(z) by convert to complex with tocomplex(x)
Input your function, click the complex2D button. e.g.
16. complex2D(pow(x,x))
More in complex2D 2 curves of real and imag parts

### in complex domain

Input your function, click the complex button. e.g.
17. complexplot(z)
Input your function, click the complex3D button. e.g.
18. complex3D(pow(x,x))
Riemann Surfaces. e.g.
19. complex3D(pow(x,x))

More in complex function

### in WebXR domain

20. color WebXR surface of complex function on complex plane

## References

1. complex - complex function - complex math
2. math handbook chapter 10 complex function
3. complex animate(z) for phase animation, the independent variable must be z.
4. complex plot(z) for phase and/or modulus, the independent variable must be z.
5. complex2D(x) for complex 2 curves of real and imag parts, the independent variable must be x.
6. complex3D(x) for 3 dimensional graph, the independent variable must be x.
7. color WebXR surface of complex function on complex plane
8. Riemann surface - Complex Branches - complex coloring
9. 2D surface - 3D surface
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