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1. What are Time Scales?
2. Definition of a Time Scale
3. Notation
4. Differentiation and Integration on Time Scales
5a. Operations Applet

6. The Time Scale Exponential

6a. Applet Examples


    6a. The Time Scale Exponential: Applet Examples


    This Applet illustrates time scale exponentials on some selected time scales.


Applet Instructions:

  1. Use the pull down menu labeled Select Time Scale: to select a time scale to graph.
    1. Discrete D[1:10] -- A discrete line with points at every integer from 1 to 10.
    2. Continuous C[1:10] -- A continuous line between 1 and 10.
    3. D[1:.2:6],C[6:8],D[8:15] -- A line with a discrete section from 1 to 6 with points 0.2 apart, a continuous section from 6 to 8, and a discrete section from 8 to 15 with points every integer.
    4. Log Time Scale -- A logarithmic line from 0 to about 2.4
    5. P(a,b) Time Scale -- A time scale with 5 sections; each section contains a continuous (a) region and discrete (b) region.
    6. Rand. D[0:rand(1,2):20] -- A discrete time scale with a random mu value between 1 and 2
    7. Rand. D[0:rand(1,5):20] -- A discrete time scale with a random mu value between 1 and 5
  2. Input an exponent (any real decimal number will do, although negative numbers are usually more exciting) in the box labeled Set Exponent:
  3. Press the Plot button to display the selected options in the graphing region.

Extra Options:

  • Use the Toggle Axes check box to display or remove the axes lines for easy viewing of a particular time scale's shape.
  • Use the Toggle Continuous check box to display the continuous time scale on the graphing region for comparison against the currently selected time scale.
  • Press the Reset button to return the settings to default: a discrete time scale with an exponent of 2.
  • Use the mouse coordinates located at the bottom left of the applet to explore the graphing region accurately.

Specialty Options:

Select the Log Time Scale option from the pull down menu and press the plot button. You will see more buttons appear on the control panel.

Graphs the log time scale from exponent = -1 to exponent = -300 consecutively. Notice what happens to the log time scale as compared to the continuous timescale.
Stops the animation to allow for more precise interaction with the animating process.
Starts the animation from the currently graphed exponent. Use the Start button to watch the animation run from the current exponent to -300.
Step a stopped animation forward (in a more negative direction) by one whole number.
Step Back
Step a stopped animation backward (in a more positive direction) by one whole number.

Select the P(a,b) Time Scale option from the pull down menu and press the plot button. You will see a slider appear on the control panel.

As the slider's label might suggest, changing the location of the slider will increase or decrease the ratio between the a and b sections of the time scale. At 0% visibility, a appears almost as a completely discrete time scale. With 100% visibility, the P(a,b) becomes a continuous time scale (use the Toggle Continuous check box for comparison).



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