Differential Equations - Dynamic Models
A Theoretical Introduction to Dynamic Models
I. Dynamic
Ordinary Wolfram Language sessions consist of a series of static inputs and outputs, which form a record of calculations done in the order in which they were entered.
In[1]: x = 5;
In[2]: x2
Out[2]: 25
However, you may often want a fundamentally different kind of output, one that is automatically updated to always reflect its current value. This new kind of output is provided by Dynamic.
Evaluate the following cell; note that the result will be again 25 because the current value of x is 5:
In[1]: Dynamic[x2]
Out[1]: 25
But if you subsequently change the value of the variables, the displayed output will change retroactively.
In[2]: x = 7;
Note that Out[1] automatically changed to 49.
Practice with different dynamic objects in the following notebook:
DynamicModules1 
II. Sliders
This associates the position of the slider with the current value of the variable x.
In[16]: Slider[Dynamic[x]] 
In[17]: Dynamic[x]
Out[17]: 0.15
Drag the slider around. As the slider moves, the value of x changes and the dynamic output updates in real time.
The great power of Dynamic lies in the fact that it can display any function of x just as easily.
Dynamic graph with slider controlled frequency:
Dynamic binomial expansion with slider controlled exponent:
This changes the disk color:
In[63]:= Clear[ red ];
Slider [Dynamic[red] ]
Graphics[ {RGBColor[Dynamic[red], 0.5, 0.5], Disk[ ] }]
Out[63]:=
*** Make three sliders with red, green, blue variables to control all components of RGB color directive.
Practice with different sliders in the following notebook:
DynamicModules2