Solution of the heat problem- One end insulated, other end fixed temperature

In Section 2.5, the following heat problem is solved

   
   
   

with solution

   
    where      

Here are animations of the solution with parameters a = 1 and k = 1 for the time t = 0 to 1.
On the left is an animation with equally spaced times from t = 0 to 1.
On the right, the animation uses logarithmically spaced times. This makes it easier to see how the solution changes at times near 0.
Notice that the slope at the right end is always 0.