Thursday, January 10, 2013

Down, Down, Down in a Freezing Ring of Ice

Non-calculus limit problems are fantastic for reinforcing the conceptual aspect of new physics principles. Nick Weckesser, an old college buddy, came up with this one and it remains one of my favorite. And as always, enjoy!

"F@#$ it! We'll do it live!"

Inspired by O'Reilly's viral rant and the prolific work of YouTuber PatrickJMT, I decided to experiment with a different format: live voice-over with minimal editting. The pros: no post makes cranking out videos a cinch. The cons: the videos are far less polished, and possibly less effective in conveying the information.


How to Row Reduce like Dr. Seuss

Oh, all those numerous and nasty equations!
All the plugging and chugging, it takes too much patience.
I've got just the thing for such an awful occasion:
It's mighty, it's sleighty! It's Gauss-Jordan Elimination!
First, our equations enjoy preparation.
Each variable is queued in ascending gradation.
Once aligned and accounted, their nice numeral agents,
Get bumped to a matrix in corresponding locations.
Next, we apply a few matrix operations:
Addition and subtraction. Division, multiplication.
Yes, our rows are massaged with arithmetication,
Until they're reduced to the simplest notation.
Lo', all of our multiplex math manueveration,
Concludes with a comely, concise configuration.
The name of this sexy and subtle sophistication?
She goes by Row Reduced Echelon Formation.
To the left: a delightful diag-one-alation.
To the right: our solutions, in column notation. 
Such a time-saving tool! Such a cool calculation!
It's mighty, it's sleighty! It's Gauss-Jordan Elimation!