Physical Mathematics?

June 20, 2012 4:25 PM

Is there a book that teaches math via physics?

Plenty of physics is taught via math, right? Like, this physical concept is embodied by this formula, etc. Is there any resource that goes the other way, i.e. follows general mathematical concept introduction order (e.g. derivatives, then integrals, and so on), but ties those concepts to physical processes as it does so, perhaps making them more concrete?

posted by adamdschneider to science & nature (7 answers total)

I don't know if it meets your criteria exactly, but I read about halfway through "A Tour of the Calculus" with my math-hating, physics-loving son to help teach him some math and convince him math was his friend.
posted by Michele in California at 4:35 PM on June 20, 2012

Quite a few calculus books do this! Rule of thumb: the larger, heavier, more picture-filled, and less yellow a calc book is (Serge Lang, I'm looking at you), the more likely it is to have a lot of story problems. A large fraction of those are likely to be based in physics (mostly mechanical, but you definitely get some E/M stuff in e.g. Stewart).
posted by AkzidenzGrotesk at 4:52 PM on June 20, 2012

There is a set of textbooks which go through a course of "mathematical physics". The course is different mathematical techniques (primarily in calculus) and all of the illustrations are physics problems. The one we used the most when I was in school was Arfken.

Link

(Thirty years and four editions ago that was considered the best though there likely are better ones now.)
posted by bukvich at 5:17 PM on June 20, 2012

I think most physics classes also teach the math as they go, even if it's only on a cursory level, or as review. I don't think you'll really learn the math completely that way, but it's usually enough so that you can follow along with the relevant material. At least the iTunesU classes I've watched on physics all do, and so do the khan academy physics videos.
posted by empath at 5:55 PM on June 20, 2012

The Mathematical Mechanic: Using Physical Reasoning to Solve Problems
posted by ellenaim at 6:19 PM on June 20, 2012

What level of math do you want? This may be higher than you need, but I gotta say, I never really understood the hard parts of multivariable calculus until I read Purcell's Electricity and Magnetism (and I am a 100% pure mathematician who doesn't even like physics.) I also really like Sternberg's Group Theory and Physics. (This corresponds roughly to a course that would be called "Abstract Algebra" -- usually taken after multivariable calculus, but for many people substantially easier.)
posted by escabeche at 6:53 PM on June 20, 2012

The one we used the most when I was in school was Arfken.

*grimace* Arfken is a bit advanced, save that for learning bessel functions, not intro calc.

Try an intro physics book, of the sort used to teach physics to first-years in the major.
Halliday and Resnick, Physics, 3rd Ed, teaches the derivative when it teaches the concept of velocity, and introduces the integral with the copy of work. Tipler, Physics - extended version, 3rd Ed, teaches the derivative when it teaches the concept of velocity and introduces the integral a short bit later at the end of that section on motion in one dimension.

Either one should be fine; and cheap. Get the 1990, 1991 version; newer ones may have a more info-box filled style which can be tedious.
posted by sebastienbailard at 7:23 PM on June 20, 2012