in which I divulge great nerd secrets
it's about math this time
First of all, if you took college calculus from a book that was the size of a medium-sized dictionary, you got ripped off. You should write the professor and ask for your tuition back. High school, this is not so bad, if you think everyone should graduate from high school.
The text they used to use at Caltech and MIT is Tom Apostol's Calculus I and II. Other textbooks in the same class are Courant (who was one of David Hilbert's students) and, I am told, one by Spivak. I don't know who uses what these days. Incidentally, these textbooks are apparently avidly traded and distributed in e-book format by students in the countries some people like to worry will bury us.
Apostol's Calculus I famously has 666 pages: we called it "the false Apostol".
Since I stumbled across an easy integral I needed to solve, for the first time in literally years, some months back, and had to run to a table of integrals squealing like a little girl because I'd forgotten everything I ever new about solving integrals except looking them up, I've made my old calculus textbook my bathroom reading. I'm about a third of the way through. I can tell you, the mathematical style of exposition is really pleasant when the pressure's off.
One thing I've learned so far that I wish I knew then: know your trig identities and basically everything else you should know about transcendental functions cold. Especially the things you use less often, like double, triple, half angle formulas, sum and difference formulas, and so on. Yes, you can always look them up, but I remember suffering over problems in my later undergrad years that basically involved recognizing that kind of thing.
Also you can solve a lot of definite integrals you'd think you'd need to trot out integration by substitution or by parts or such, just by invariance under translation or expansion/contraction.
But now, for what you really want to know.
How to fake all the math you'll ever need:
The 1% case: they will want to prove they're even smarter than you, and will then just solve the problem for you.
If someone calls your bluff or tries this on you: Say: "Hrm, how do you set up the boundary conditions for that, then?" This is just a really good question to ask anyone doing any kind of analysis, anyway.
First of all, if you took college calculus from a book that was the size of a medium-sized dictionary, you got ripped off. You should write the professor and ask for your tuition back. High school, this is not so bad, if you think everyone should graduate from high school.
The text they used to use at Caltech and MIT is Tom Apostol's Calculus I and II. Other textbooks in the same class are Courant (who was one of David Hilbert's students) and, I am told, one by Spivak. I don't know who uses what these days. Incidentally, these textbooks are apparently avidly traded and distributed in e-book format by students in the countries some people like to worry will bury us.
Apostol's Calculus I famously has 666 pages: we called it "the false Apostol".
Since I stumbled across an easy integral I needed to solve, for the first time in literally years, some months back, and had to run to a table of integrals squealing like a little girl because I'd forgotten everything I ever new about solving integrals except looking them up, I've made my old calculus textbook my bathroom reading. I'm about a third of the way through. I can tell you, the mathematical style of exposition is really pleasant when the pressure's off.
One thing I've learned so far that I wish I knew then: know your trig identities and basically everything else you should know about transcendental functions cold. Especially the things you use less often, like double, triple, half angle formulas, sum and difference formulas, and so on. Yes, you can always look them up, but I remember suffering over problems in my later undergrad years that basically involved recognizing that kind of thing.
Also you can solve a lot of definite integrals you'd think you'd need to trot out integration by substitution or by parts or such, just by invariance under translation or expansion/contraction.
But now, for what you really want to know.
How to fake all the math you'll ever need:
- Get a copy of Abramowitz and Stegun, the Dover edition, it's like $20. Use an online edition if you're really cheap and can stand the hassle. The tables are kind of worthless these days but at least you'll be ready to do real science and engineering on a four-function calculator or an abacus if the big one hits. The rest is well worth your double sawbuck, as an amazon reviewer writes: "un grimoire mathématique unique en son genre!"
- Go through and learn what each of the special functions and such that it has tables for are used for in practice. You can do this with google. Also, chapter 4 has all the trig identities and such you will ever need to know. As above. Memorize them.
- Then you can just blithely say things like "well, it's propagating down a cylinder, right? so it's going to be described by bessel functions of the such-and-such order..."
The 1% case: they will want to prove they're even smarter than you, and will then just solve the problem for you.
If someone calls your bluff or tries this on you: Say: "Hrm, how do you set up the boundary conditions for that, then?" This is just a really good question to ask anyone doing any kind of analysis, anyway.