Home > The Web (Blogs, Forums, etc) > WolframAlpha – answering the unanswerable

WolframAlpha – answering the unanswerable

I had a funny experience with WolframAlpha recently. I typed in:

differentiate (t-t^2/2)Heaviside(t) at t=0

and the result was (as you can probably see in the link):

 

$\theta(0)\approx\theta(0.)$, alternate form $1$

Surprise, surprise. The function obviously doesn’t have a derivative in that point, but WolframAlpha bravely calculates it. I tested Mathematica 7 with the same question, using both UnitStep and HeavisideTheta for the unit step function. The difference between these two is that HeavisideTheta implemented in Mathematica is undefined at 0, while the UnitStep’s value at 0 is 1.

Heaviside theta case:

In[1]:=  D[HeavisideTheta[t] (t – t^2/2), t]

Out[1]:= (t – t^2/2) DiracDelta[t] + (1 – t) HeavisideTheta[t]

In[2]:= % /. t -> 0

Out[2]:= HeavisideTheta[0]

As noted, HeavisideTheta[0] has no defined value.

Unit step case:

In[1]:= D[UnitStep[t] (t – t^2/2), t]

Out[1]:=(t – t^2/2) (\[Piecewise] {{Indeterminate, t == 0},{0, \!\(\*TagBox[“True”,”PiecewiseDefault”,AutoDelete->False, DeletionWarning->True]\)} }) + (1 – t) UnitStep[t]

In[2]:= %/.t->0

Out[2]:=Indeterminate

This opens few other questions about these calculations, but I’ll stop right here.

Advertisements
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: