College Math Teaching

September 5, 2010

Calculus in the News

Filed under: calculus, derivatives, media, news — collegemathteaching @ 9:55 pm

Can you spot the use of the derivative (calculus derivative) in this Paul Krugman post?

Delusion #2 is the belief that the stimulus may yet do the trick, because there are still substantial funds unspent. I tried to deal with this last year. The level of GDP depends not on total funds spent, but on the rate at which funds are being spent, which has already peaked; GDP growth on the rate of change in the rate at which funds are being spent, which peaked last year. It’s all downhill from here.


March 6, 2010

Calculus in the News: the Obama Administration’s Job Loss Graph

Filed under: calculus, derivatives, inflection points, media, news — collegemathteaching @ 9:43 pm

Derivatives in the news

The Obama administration has been touting this graph:

The data for this graph is taken from here and here.

So what does this graph show? The graph shows the job losses per month (non-farm jobs, adjusted for seasonal effects) with the upward bars representing job gains; one can clearly see that the economy is losing fewer jobs per month now than it was prior to the stimulus bill being signed. In short, this is the graph of the rate of change of the number of jobs per month; in short, this is a calculus derivative.

In “line” format the above graph corresponds to this one:

So, what does the actual jobs graph look like? Here it is (graphed in a “smoothed out” form):

Note: the vertical line signifies when the stimulus bill was signed into law (February 17, 2010). The units are in thousands.

Of mathematical note is the “negative peak” of the jobs loss graph: it corresponds with the change in the concavity of the jobs graph; the graph goes from being “concave down” to being “concave up”. Of course, the hope is that the jobs graph will eventually go up and not merely level off.

Of course, it is possible for jobs to go up and unemployment to go up at the same time, say, if jobs are being created more slowly than the workforce is expanding.

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