Sanity Checks are missives on a specific math point in need of clarification. I try to do so using the fewest words possible. Usually, this is still quite a few words.
Today, just a brief browlf to pass along an alternative notation for integration by parts I recently stumbled across (in Weinstock's book on variational calculus, but no matter). It's not necessarily earth-shaking. But to me, it makes much more sense and is easier to remember than the usual bark bark about u dv's and v du's and writing them in a little rectangle and connecting everything with dotted lines.
As Weinstock puts it, IBP simply lets you swap derivative terms under the integral sign:
You may prefer the some-other-way you remember IBP. If so, no worries: I still like you. But after decades of my defective calculus psyche laboring under the dotted line box thing,Weinstock's notation was like a little splash of sunlight breaking through the winter clouds, a promise of girls in convertibles and green things pushing their way through the Circle Pines hardscrabble.
Today, just a brief browlf to pass along an alternative notation for integration by parts I recently stumbled across (in Weinstock's book on variational calculus, but no matter). It's not necessarily earth-shaking. But to me, it makes much more sense and is easier to remember than the usual bark bark about u dv's and v du's and writing them in a little rectangle and connecting everything with dotted lines.
As Weinstock puts it, IBP simply lets you swap derivative terms under the integral sign:
You may prefer the some-other-way you remember IBP. If so, no worries: I still like you. But after decades of my defective calculus psyche laboring under the dotted line box thing,Weinstock's notation was like a little splash of sunlight breaking through the winter clouds, a promise of girls in convertibles and green things pushing their way through the Circle Pines hardscrabble.
No comments:
Post a Comment