Post
by djh101 » Sun Dec 07, 2014 2:47 am
Minimal Requirements:
-Classical Mechanics- Taylor seems to be popular. I used Marion & Thornton and didn't care too much for it, although the section on Lagrangian mechanics was alright.
-Calculus- Thomas or Rogawski will do just fine.
-Linear Algebra- Poole will cover the basics.
-Ordinary Differential Equations- I don't remember what book I used for this. Tenenbaum is pretty decent, though.
-Mathematical Methods- Boas covers pretty much all the math you'll need as a physics major- ODE, PDE, Fourier series. It's more of a junior level book, though.
Very Well Off:
-Classical Mechanics- Goldstein is the standard graduate text (although some people use it either as their main book or a supplement in undergrad) and a pretty good book on the subject. Landau is another acclaimed graduate text. I haven't read it myself, but do plan to purchase it as soon as a copy goes up on Amazon for under $30.
-Linear Algebra- Shilov covers upper division linear algebra very well, although the book is somewhat dense and hard to follow without some mathematical maturity. One downside is that inner product spaces aren't covered at all. Friedberg was who we used for my linear algebra course and I would recommend it as well.
-Vector and Tensor Analysis- Pick up Borisenko's book. You'll thank me later. I've had a very hard time wrapping my head around wrapping my head around transformations written as summations.
-Real Analysis- You can do without it as an undergraduate, but good to know (more relevant once you get to graduate level physics). There's plenty of books on the subject and I'm not sure I really have one to recommend. If you're interested in set theory, though, Stoll has a nice introduction to integers/rational numbers/real numbers.
-Complex Analysis- Boas covers the basics. I can't recommend any specific book. Not a bad topic to be familiar with.
Overkill:
-Advanced Linear Algebra- Pick up Roman. There's no such thing as too much linear algebra.
-Abstract Algebra- Pinter. Only really needed as a prerequisite for reading Roman. It is my favorite Dover book, though, and I'd highly recommend it if you're interested in the subject for whatever reason.
-Functional Analysis- Kreyszig. Pretty much just more linear algebra but with a different name. Very relevant to quantum mechanics.
-Partial Differential Equations- Farlow. Probably my second favorite Dover book. You'll cover all the PDE you'll need as an undergraduate with Boas, but PDEs are good for you.
Summary: A good calculus background is as necessary as knowing how to count (up to multiple integration; divergence and curl and Stoke's Theorem are still necessary but slightly less necessary). You'll want to supplement your standard calculus curriculum with at least the basics of ordinary differential equations (separation of variables, existence/uniqueness, method of undetermined coefficients). As you get higher up in physics it will become less calculusy and more linear-algebraey, so basic linear algebra is also absolutely necessary. As things start getting quantumy, the stronger your linear algebra background the better. Tensors, Fourier series, PDEs, etc. are all good topics to know but not as universally applicable as calculus and linear algebra (i.e. you won't be using them everywhere and all the time).
