- Jun 30, 2012
Jameson,Moving beyond memorizing formulas on faith and starting to prove them or follow a proof is a great feeling. Whenever I tutor math at any level I almost never suggest memorizing something, instead reinforce concepts that apply to many formulas and situations. Most of the time it doesn't work that well - either the student wants a list of "tricks" or the approach needs more time to sink in. I've seriously read through solution manuals for a university entrance exam that say something like "Using tactic D-15 from this book the solution is ________". Anyway, I digress.
The last bit of your integral calculation 2 and 2/3 u-squared. Two things:
1) Where did the u^2 come from?
2) Why did you convert the fraction to a mixed number? Leaving it as an "improper fraction" is perfectly fine and the standard way to write a fraction unless told otherwise. Maybe you wrote it that way to show the area was between 2 and 3 square units.
I tried writing a mixed number in Latex just now but the spacing wasn't right.
1. I thought that because what I have integrated is essentially an area that it should be written as squared units (since the unit of measurement isn't otherwise stipulated)
2. thanks for the tip regarding mixed fractions; duly noted!
"Using Tactic D-15 ..." You encapsulate my distaste for modern teaching methods so nicely! (perhaps D-13, for Doom-13 would have been even better)
I'm sure I'm not telling you anything you don't know here: words carry not only meaning but the history of the meaning(s) as this/these evolve in time. If one throws out words and names of theorems for an algorithmized (pardon the neologism, but it is almost apt to my point here) for a computerized way of communicating, let alone teaching!, well then, the memory of civilization itself is imperilled by a kind of cultural and intellectual Altzheimer's.
Momentarily gloomy ("this too shall pass" )