Good Physics Books For a Math PhD Student?

An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?"

Comments

I'm gunna say this once..

[QuantumG]

Get back to writing your thesis.

Slacker.

Books

[TheEldest]

They Feynman Lectures on Physics would probably be a good place to start. It'll be basic to advanced.

http://www.amazon.com/Feynman-Lectures-Physics-including-Feynmans/dp/0805390456/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1226900482&sr=8-2

If you want something more specific, to a topic, there will be a slew of books. I found some pretty good ones following links on Amazon from one to another and reading reviews.

Re:Books

[TheEldest]

I just thought of another one. It's Mathematical Methods for Physicists by Arfken. I wouldn't necessarily recommend buying it, but find one you can flip through (most university libraries have it, as do most math/physics department libraries. and I can almost guarantee that someone you know has this book).

http://www.amazon.com/Mathematical-Methods-Physicists-George-Arfken/dp/0120598760/ref=sr_1_5?ie=UTF8&s=books&qid=1226903092&sr=1-5

It's a math text, but since it's geared as a math text for physicists, the explanations may have the right amount of physics in them.

(I've always liked it as my math reference).

Though, I don't think this will be at your level (probably below), but it may help with the ground work. As I said, don't buy it, but find a copy to flip through.

PDEs now?

[Anonymous Coward]

You are in your third year of a PhD program and are only now studying PDEs? Aren't they more of an undergrad topic, or have schools gotten weaker? :)

p.s. First post!

Re:PDEs now?

[krull]

You both probably studied how to solve certain simple PDEs in simple geometries (like the heat, wave, and Poisson equations). At a graduate level one normally learns how to prove existence and uniqueness of solutions to PDEs, how smooth those solutions are (i.e. how many derivatives do the solutions possess), and how to define weak forms of PDEs for which non-classical solutions exist (solutions that are not necessarily even continuous). Then there is the whole area of non-linear equations which is a very active research topic... (See the Navier-Stokes Equations.)

Re:PDEs now?

[NewbieProgrammerMan]

There can be a world of difference between graduate and undergraduate PDE courses; it's not like everything that's known about PDEs can be taught in a couple of undergraduate semesters. I expect most undergrad PDE courses are geared towards showing you the methods that work for a few classes of linear PDEs; a graduate course might be concerned with the analytical underpinning of those methods, or maybe about numerical and analytic techniques that are useful in solving classes of nonlinear PDEs, etc.

That being said, though, from the way the original question is worded, it sounds like it's the first time this person has seriously encountered PDEs. Not having this happen until the third year of a PnD program does seem a little odd.

p.s. No, you're not.

Re:PDEs now?

[Anonymous Coward]

PDEs are not normally part of a math degree. They do form the central basis to applied math degrees. People in the engineering and physical sciences have a great understanding of applied math, but they have little to no understanding of pure math. If you get a BS in a physical science or a BE from any decent university, you will basically have a minor in applied math (adv. calc, ODEs, PDEs, probability, statistics, nonlinear dynamics, complex analysis, and calculus of variations). But you have not even scratched the surface of pure math. Mathematicians worry primarily about pure math. To teach PDEs would be insulting to them due to its lack of generality. As many physicists and engineers have learned over time, if you have a difficulty in understanding mathematics that applies to your field, the worst person you can go to for help would be a mathematician that hasn't studied applied math. The best person you could go to would be a mathematician who specialized in applied math.

Some essentials

[Anonymous Coward]

Goldstein, Classical Mechanics. Standard grad level mechanics, solid book, mathematically rigorous yet still intuitive.

For EM and Quantum, even a math grad should read the advanced undergraduate books by Griffiths:
Introduction to Electrodynamics
Introduction to Quantum Mechanics

For thermodynamics, I don't know the best text.

For General Relativity, the standard undergrad book is Hartle's Gravity. But since you're a math PhD, you can go straight to the finest first grad level Relativity book by Sean Carroll:
Spacetime and Geometry

If you're looking for intuition, the indispensable and invaluable books are Feynman's Lectures on Physics.

I can recommend mathematical physics texts, but I get the impression you want the missing background for understanding. Hope this is helpful.

Some recommendations from another Math Ph.D

[tehgnome]

Most of the previous comments have been far too elementary. I too am a math Ph.D. student and I understand what you are looking for as for while I was working in mathematical physics on loop quantum gravity. Here are some big ones; -classical mechanics has one resounding answer http://www.amazon.com/Mathematical-Classical-Mechanics-Graduate-Mathematics/dp/0387968903/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1226901309&sr=8-1 -for quantum theory and such use http://www.amazon.com/Quantum-Physics-Stephen-Gasiorowicz/dp/0471057002/ref=sr_1_1?ie=UTF8&s=books&qid=1226901473&sr=1-1 -for GR and such http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/ref=sr_1_1?ie=UTF8&s=books&qid=1226901528&sr=1-1 I dont know a good thermal book, but I am sure you can come up with one. By the way, there was a very similar ask slashdot during the summer from an astronomer asking for the same thing. good luck and I dont know what you research field is, but in general a great read if you are in algebra is the book on quantum groups by Majid. This has a nice physical perspective on the objects. http://www.amazon.com/Foundations-Quantum-Group-Theory-Shahn/dp/0521648688/ref=sr_1_4?ie=UTF8&s=books&qid=1226901678&sr=1-4

Re:Man...

[JeanBaptiste]

No, I'm in the exact opposite situation. I don't know anything about PhD level math _or_ physics.

They're All Targeted for Mathematicians

[w8dm4n]

I've a couple of degrees in Physics, and I assure you, half the print in the _vast_ majority of Physics books is equations. Most physics texts seem to assume a math minor. Most Physics majors first see partial differential equations, special functions, and group theory as undergraduates. A couple of friends took partial diffeq for fun. Yeah, that's one way to know you're a nerd.

I suggest a library or a used bookstore, as these things are expensive. Here are some of the typical texts you see around on various physics topics (by author's name, because the titles are useless):

Electromagnetism:
    Griffiths is a really great undergrad book, which is easy to read.
    Jackson is the classic first semester grad-school book.
Math Methods of Physics:
    Arfken is a classic.
    Cantrell is an up and coming variant.
Thermodynamics:
    Kittel is an oldie, but a goodie. Someone else prolly has a better suggestion.
General Undergrad Phenomonology:
    The World Wide Web - Invented at CERN, y'know.
    Halliday & Resnic is probably the easiest book to find.
    Serway is newer.
Relativity:
    Rindler is the standard.
Mechanics:
    Goldstein is pretty easy to find.
Quantum:
    Landau (yep, the same) and Lifshitz is a solid text that
              hits on Shcrodinger's equation well.
    Griffiths is easier to read, as is Eisberg & Resnick.
Modern Physics:
    Less of an obvious choice, but it'll be a good source for more sexy topics.

A lot of partial diffeq is used in mechanics. IIRC, partial diffeq was invented to describe mechanical systems, so many of the examples are very intuitive (for you of course, not for 99.9% of the population.)

Interestingly enough, this Wikipedia link http://en.wikipedia.org/wiki/Partial_differential_equation can take you many places, as it seems to come from the mind of a physicist more than a mathematician.

Alternately, you will probably have success finding a physics student at your relative level that has the intuitive feel, but is weak on math. You could quite a bit from each other in short order.

may the electromagnetic force be with you,

-Rick

   

Re:3rd year PhD student taking PDE?

[MPolo]

This kind of reminds me of the comments I got from Business Calculus students when I was carrying around my graduate Algebra book, which was appropriately titled "Algebra". "Oh, Algebra! I had that in High School. It's not so hard..." If only they knew what was inside that bright lemon-yellow cover...

Re:Standards have slipped then...

[Scott Carnahan]

I graduated in 1985 with a BS in Math & Chemistry. Partial Differential Equations was a required course back then, and the school I attended was nothing special in terms of what they required.

PDE is intermediate level calculus.

This might come as shocking news to you, but the typical undergraduate PDE class only scratches the surface of a rather deep and broad subject. From the examples you list, it seems that you only worked with equations for which global existence and regularity are trivial, and you have lots of conserved quantities. Many aspects of PDEs are fields of active current research, including heuristics for fluid mechanics modeling, theoretical questions concerning geometric structures on manifolds (see Yang-Mills or Seiberg-Witten equations), and integrable hierarchies. I'm not a specialist in PDEs, but I'm sure there are others who can list much more, and describe interesting open problems in detail.

Also, I should point out that the lack of a required PDE class does not necessarily mean standards have slipped. If you look at the requirements for a major in the top math departments in the US, you'll find that they have few required courses, and many options. I think these departments have decided that students should have freedom to focus on their interests after they have learned some fundamentals, and that there are other areas of mathematics, such as abstract algebra, topology, and combinatorics, that may hold their interest. I have met many mathematicians who have little experience with even the heat and wave equations, and they have done fine, because their work was not related to these questions. It is possible that the OP has taken a similar educational track.