This is a partial Fourier series solution of the the one-dimensional heat equation with a zero left boundary and a Newton's Law of Cooling style right boundary condition. The sliders allow one to vary a few important physical parameters. Once the parameters are chosen, one can advance the solution in time with the [math]t[/math] slider. [br][br]The problem is based on Example 7.1 from Farlow's "Partial Differential Equations for Scientists and Engineers".
What is the effect of varying [math]h[/math]?
In the "three dot" menu at the upper right most corner of the page, click on "Open with GeoGebra App". This will allow you to modify elements of the visualization. [br][br]Click on the definition of [math]\varphi[/math] in the left hand panel and change it to [math]\varphi\left(x\right)=5x\left(1-x\right)[/math]. What's interesting about the behavior of the temperature at the right end as time moves forward? How is this behavior affected by the value of [math]h[/math]? Explain the behavior from a physical perspective.