for Macintosh and Windows
What's new in Version 4
- Graphing data
- Graphing 3D points
- Graphing surfaces of revolution
- Graphing ordinary differential equations in 3D
- Specify ODE initial conditions
- Tube plots
- Numeric Integration
- New functions
- Long variable names
- Universal binary on Mac OS X
- Support for multiple processors
What was new in Version 3.5
- Parameter sets
- Native Mac OS X application
What was new in Version 3.2
What was new in Version 3.1
- Complex numbers
- Color maps in 2D
- Point plots in 2D
- Vertex lists in 4D
- Parametric curves in 4D
- Parametric surfaces in 4D
- Examples menu and sample documents
- New functions
- Text expressions in coordinate ranges
- Direction fields
What was new in Version 3.0
- Text comments in documents
- Multiple document windows
- Save as web page
- Save as RTF for export to word processors
- 3.0 acts as a helper application for GC documents posted to the web
What was new in Version 2.7
- Change the 3D background color
- Define functions and variables symbolically
- Copy and paste formulas as plain text
- Equations now line-break and scroll
- 1st order ordinary differential equations in 2 dimensions
- Correct handling of fractional powers
- New functions
You can enter tables of data, numerically transform the data, and graph data in two and three dimensions.
You can rotate a curve around an arbitrary axis to generate a surface in three dimensions.
You can graph ODEs in three dimensions.
You can specify initial conditions for ODEs by giving starting points on surfaces.
Vector fields can be graphed on surfaces.
You can use Graphing Calculator 3.1 as a calculator for complex numbers. For example:
A complex function of a real parameter, t, specifies a curve in 2D. For example:
This is a shorter way of writing the parametric equation:
You can also use z as shorthand for x + iy. For example:
A complex function of a real parameter, z, specifies a curve in 3D. Observe that this is the same complex function as in the 2D example above, but here the parameter z is used as the third 3D coordinate.
This is similar to writing the parametric equations:
You can also write parametric equations for curves in four dimensions by specifying functions (which have real values) for each of the four spatial coordinates x, y, u, and v. For example:
Using z as shorthand for x + iy, you can graph 3D surfaces representing complex functions. For example:
In this example, observe the four zeros at +1, -1, +i, and -i.
Using z as shorthand for x + iy, you can graph 3D surfaces representing complex functions. The height of the surface represents the magnitude of the complex function. The phase of the complex function is encoded in the color of the surface. For example:
A complex function f(x + iy) depends on two real parameters x & y and has two components, Re f, and Im f. We can render this as a surface in 4 spatial dimensions with coordinates:
(x, y, Re f(x+ iy), Im f(x + iy)) and then project this surface to the screen in a manner similar to the way we project 3-D surfaces onto a 2-D screen. Note that in the following, z=x+iy and w=u+iv.
In the following example, you can drag the purple dot, which moved the square grid along with it. The blue grid is the map of the square grid under the complex function f(z).
You can specify the color at each point in the place by giving functions for either the (red, green, blue) or the (hue, saturation, value) components of the color.
In the following example, as n varies, the point traces out a circle:
The following shows a hypercube in four dimensions specified by writing the 32 edges between its 16 vertices.
This is the parametrization for a flat torus in 4D. It is the product of an x-y circle (sin u, cos u), and a u-v circle (sin v, cos v). (The four 4D coordinate axes are x, y, u & v. The letters u & v are also used separately for the surface parametrization. This is confusing as u and v must be interpreted differently depending on context.)
Type command-option-d to draw unit vectors in a vector field.
Version 3.1 ships with example and template documents which are also accessible from the new Examples menu.
The preferences dialog now gives control over the background used with 3D objects.
(You must type "f control-9 x" to distinguish f(x) as a function.)
Copy as Text on produces sum(x^k/k!,k=0,5).
Fractional powers of negative numbers are handled properly now.
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