Math Tricks Coffee Mug

Nothin' goes with the mathefying like a good cup of whatever, and for the duration of this discussion we'll just assume "whatever" = "coffee" 'cause everything else you nerdozoids drink has a trademarked brand name that we can't mention on Zazzle lest the corporate lawyers descend on us like turkey vultures. Anyhoo, if you are going to derive it behoves you to keep some ideas handy for when you get stuck (and if you're anything like LabKitty, for "when" read "invariably"). Sure, you could just keep a list of crux moves in your head, but if you're going to drink and derive, you may as well emblazon those handy tips on a flagon. Enter the LabKitty Math Tricks mug. A veritable rogue's gallery of tricks, tips, ruses, ploys, schemes, contrivances, machinations, centrifuges, and chicanery, any one of which might be all that separates a morning spent shaking with rage from one spent drawing so many Halmos symbols that your notebook looks like the nose of a WW-II fighter after a dogfight with a squadron of magic carpets. No doubt you recognise a few of these rascals. For example, proving a function is equal to one by proving the square is equal to one (plus a switch to polar coordinates) is how you show the Gaussian distribution is normalised. Functions of different variables both being equal to the same constant pops up in separation of variables when solving the wave equation. And if we remember our relativity, you use a (1 + nx) substitution for (1 + x)^n in the derivation of e = mc2. This last example is of course just one application of the grandaddy of them all: taming some uppity junk by substituting a Taylor series and throwing out all the higher-order terms. This trick is used so often we have embiggened it on the design to emphasize just how often it will save your bacon. As the cool kids say: quod erat demonstrandum.