# blueollie

## And the Laplace Transform offends…

This Friday, we start Laplace Transforms in differential equations. By “Laplace Transforms”, we mean the usual simplified Laplace Transform we teach to beginning differential equations students; we do not know what a Lebesgue or a Stieltjes integral is.

That reminded me of what happened in my first differential equations course, back in the fall of 1978. I was sitting next to Vince and the instructor wrote the following on the board:

That, of course, is the gamma function (think of it as a way to extend the factorial function into a continuous function on the reals, though there is a more general version). If you must know, for positive real numbers, $\Gamma(x) = \int^{\infty}_0 t^{x-1} e^{-t} dt$. This is a convergent improper integral for $x > 0$

Never mind that.

Vince said “box of x, what is box?” I replied “that is the gamma function, Vince”.

“Box…what’s box? They are just making stuff up! They are making it up as they go along!” Vince was just so offended by the gamma function!

Anyway, that is a memory that made me chuckle; and yes, Vince ended up passing the course.

Workout notes: Not sure what was wrong; my nose is runny and I had a tough time breathing in the gym as the pace got harder (heat? dehydration? allergies?) So my planned 10 minute warm up, 10 x (2:30 at 6.7, 2:30 at 5.3) workout became 10 minute warm up, 6 x (2:30 at 6.7, 2:30 at 5.3) followed by a 5 minute walk, then enough running to get me to 6.1 miles in 1:05, and 1:44 more of walking to get me to 10K in 1:06:44.

I call that a “rescue of a workout”; for me, a 10K training run at under 11 minutes per mile is a valid training run, and I did get some pace changes.