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Good Physics Books For a Math PhD Student?

kdawson posted more than 5 years ago | from the queen-of-the-sciences dept.

Math 418

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?"

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I'm gunna say this once.. (5, Funny)

QuantumG (50515) | more than 5 years ago | (#25782657)

Get back to writing your thesis.


Re:I'm gunna say this once.. (4, Funny)

Anonymous Coward | more than 5 years ago | (#25782673)

I'd rather not follow that advice.

Re:I'm gunna say this once.. (4, Funny)

martin-boundary (547041) | more than 5 years ago | (#25783197)

I'd rather not follow that advice.

That proves it! Only a PhD student would say that.

Books (5, Informative)

TheEldest (913804) | more than 5 years ago | (#25782675)

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

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 (4, Insightful)

ReedYoung (1282222) | more than 5 years ago | (#25782881)

I agree. I picked up the set a few years ago based on Surely You're Joking and I'd recommend them to anybody beginning in physics, especially to Professors of freshman physics, which is usually not so much taught as shoveled. The lectures are taken from his lessons in first year physics, so not too difficult for a math grad student with no previous physics.

Re:Books (5, Informative)

TheEldest (913804) | more than 5 years ago | (#25782929)

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). []

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.

Re:Books (3, Informative)

deodiaus2 (980169) | more than 5 years ago | (#25783071)

I too cannot recommend "The Feynman Lectures on Physics Vol I-III" enough. This was written for first year undergrad students, but should have been aimed for 3rd year students. It is very nice in that is very detailed, at the expense of going overboard. For example, Feynman discusses the fact that solutions to differential equations are in fact the minimal energy solutions. I did not grok this until I got to grad school and studied Finite Element Methods. Another great series is the one by Laudau and Liftshitz.

Re:Books (3, Interesting)

moosesocks (264553) | more than 5 years ago | (#25783287)

As a 4th-year Physics undergrad, I have to voice my opinion that I absolutely can't stand Feynman's texts.

They're nice to glance at, but approach the subject in a considerably different manner than any of the other renowned physics texts.

Similarly, his proofs were terse to the point of being difficult to follow. I'll admit that my mathematical intuition isn't the greatest, though I can't help but think that this was intentional on Feynman's part, as to weed out those with weak mathematical skills from his freshman lectures. This makes them rather frustrating to use as a general reference. Similarly, the texts are largely theoretical, and offer little advice with regard to problem-solving.

Personally, I've had good experiences with the Landau/Lifshitz series of texts, and it's hard to go wrong with Griffith's books on EM and QM. Goldstein's text on Classical Mechanics is also a well-known classic.

That's not to say that that Feynman's texts are all bad. Some sections are outright brilliant, and he actually takes the time to explain himself rather extensively in many sections, which many physics (and math) writers frequently neglect to do. I keep a copy of all 3 volumes on my bookshelf, as they are occasionally handy. However, I wouldn't dream of using them as my only reference.

PDEs now? (5, Insightful)

Anonymous Coward | more than 5 years ago | (#25782687)

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? (0)

Anonymous Coward | more than 5 years ago | (#25782709)

Seconded... I'm a sophomore undergrad and am taking PDEs.

Re:PDEs now? (0)

Anonymous Coward | more than 5 years ago | (#25782773)

Thirded. I took PDEs in my second year of a BSEE.

Re:PDEs now? (5, Informative)

krull (48492) | more than 5 years ago | (#25782811)

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? (0, Troll)

narcberry (1328009) | more than 5 years ago | (#25782985)

You said "stroke"

Re:PDEs now? (1, Funny)

Anonymous Coward | more than 5 years ago | (#25782997)

no he didnt

Re:PDEs now? (5, Insightful)

NewbieProgrammerMan (558327) | more than 5 years ago | (#25782861)

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? (1)

zippthorne (748122) | more than 5 years ago | (#25782955)

Unless there's some school offering a "undergrad through Ph.D" program. Then that would make sense.

Re:PDEs now? (1)

NewbieProgrammerMan (558327) | more than 5 years ago | (#25783103)

Ah, you're probably right; in that case, it's probably not too odd. :)

Re:PDEs now? (1)

narcberry (1328009) | more than 5 years ago | (#25782993)

I think what they meant was, "hey! hey! we're smart too!"

Re:PDEs now? (2, Interesting)

Secret Rabbit (914973) | more than 5 years ago | (#25783207)

No. ODE's are typical of Undergrad. But, PDE's are typical of Masters. That isn't to say that PDE's are taught in Undergrad, period. Rather that PDE's in Undergrad is atypical. At least in North America. Other parts of the world either have vastly superior high-school/Undergrad or skip a lot of the, necessary for actually understanding, stuff. Germany and China are respective examples.

3rd year PhD student taking PDE? (0, Troll)

Anonymous Coward | more than 5 years ago | (#25782699)

Huh? Why didn't you take it as an undergrad? I aced partial differential equations when I was 19.
And no, you don't need to understand the physics background. There's nothing hard about it.

Re:3rd year PhD student taking PDE? (1)

Fallen Kell (165468) | more than 5 years ago | (#25782989)

I think his problems may be the result of how the questions are being given to them. They probably won't be your standard undergrad, here is an equation, give me the answer, type, but more of the here is the situation, figure out the equation, then solve it type.

Halliday or Giancoli are nice (1)

m1ss1ontomars2k4 (1302833) | more than 5 years ago | (#25782703)

I've read through at least some of both Halliday and Giancoli, but sometimes it's nice to have someone explain things to you instead. I happened to have some very good physics professors who always explained where every equation came from (although sometimes I couldn't figure out what they were getting at until they said, "Trust me on this math here" and suddenly wrote equations on the board).

Re:Halliday or Giancoli are nice (1)

Khashishi (775369) | more than 5 years ago | (#25782853)

I don't recommend either Halliday/Resnick/Crane or Giancoli. They are both undergraduate texts treated at a rather simple level, light on math, and you'll never see a partial differential equation.

That's the problem. Most texts that are basic physics also assume basic maths.

Maybe you can handle Jackson Electrodynamics, which is a standard graduate level text. It won't be easy, but it doesn't really assume much foreknowledge, since it lays out the groundwork in the first few chapters (which are review for most students).

Re:Halliday or Giancoli are nice (1)

squidfood (149212) | more than 5 years ago | (#25782931)

I don't recommend either Halliday/Resnick/Crane or Giancoli.

I dunno, I remember finally really "getting" pdes from H&R, though maybe that was very supplemented by lectures. I do know that as subjects go, what really made the math click was E&M: Maxwell's Equations were just so damn elegant and beautiful it all came together there for me (though coffee cups are good for boundary value problems - I seem to remember Boyce and DePrima being a good text with enough of the physics to make it work well).

Re:Halliday or Giancoli are nice (0)

Anonymous Coward | more than 5 years ago | (#25783111)

NO! Giancoli is absolutely horrible. Don't ever refer to it. UCSC uses it and I hate it.

Re:Halliday or Giancoli are nice (1)

mako1138 (837520) | more than 5 years ago | (#25783267)

Giancoli isn't very good. Meh.

Making the math tangible does help (4, Insightful)

EmbeddedJanitor (597831) | more than 5 years ago | (#25782717)

If you're a practical sort of person then it really helps to understand what the math means in some sort of physical context. The academic purists be damned!

Partial differential equations (0, Offtopic)

Animats (122034) | more than 5 years ago | (#25782719)

First of all, "partial differential equations" should not be capitalized.

The general idea is straightforward. Partial derivatives are just the concept of a derivative generalized to higher dimensions. Just as a derivative is a tangent to a curve, a partial derivative is is a tangent plane to a surface.

There are many physical situations in which the physics gives you the partial derivative in the current situation, and if you want to predict what happens next, you have to integrate the partial derivative. For most real-world problems, this has to be done numerically, although for some special situations, like planetary orbits, there are analytical solutions.

Re:Partial differential equations (-1, Flamebait)

Anonymous Coward | more than 5 years ago | (#25782765)

First of all, "partial differential equations" should not be capitalized.

The general idea is straightforward. Partial derivatives are just the concept of a derivative generalized to higher dimensions. Just as a derivative is a tangent to a curve, a partial derivative is is a tangent plane to a surface.

There are many physical situations in which the physics gives you the partial derivative in the current situation, and if you want to predict what happens next, you have to integrate the partial derivative. For most real-world problems, this has to be done numerically, although for some special situations, like planetary orbits, there are analytical solutions.

ok. do you want a cookie?

Re:Partial differential equations (0)

Anonymous Coward | more than 5 years ago | (#25782907)

A partial derivative is not "a tangent plane to a surface."

Dunno why you got modded up. Basically nothing you said was enlightening or even correct, except for the contents of the first sentence.

Re:Partial differential equations (4, Informative)

VirusEqualsVeryYes (981719) | more than 5 years ago | (#25783231)

Good thing you weren't modded up. Basically nothing you said was enlightening or even correct, except for the contents of the first sentence.

You didn't even bother to correct the OP, you just sat back and decided to be a useless pedant. Yes, OP is technically incorrect, but your post is uninformative and completely worthless.

All possible partial derivatives of a point on a 3-dimensional graph fall on a tangential plane. Usually we speak of a tangent line, setting x or y constant, but if one redefines the coordinates, then any line on that plane that passes through that point is a partial derivative. So that "partial derivative plane" contains all possible partial derivatives of that point. This designation is intuitive and not particularly misleading, so there was little point in being an ass about it.

Re:Partial differential equations (0)

Anonymous Coward | more than 5 years ago | (#25783235)

He's referring to a course so it's okay for it to be capitalized, you anal retentive ninny.

Some essentials (5, Informative)

Anonymous Coward | more than 5 years ago | (#25782729)

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.

Re:Some essentials (4, Informative)

SleepingWaterBear (1152169) | more than 5 years ago | (#25782901)

I'd like to second all of these recommendations, but for Quantum Mechanics if your linear algebra is sharp, I might suggest Principles of Quantum Mechanics by Shankar.

Griffifhs' Quantum Mechanics is an excellent introduction, but it assumes relatively little math knowledge, and tends to gloss over some of the assumptions being made. This is good for a student who's going to spend most of his effort trying to learn the practical aspects of doing Quantum Mechanical calculations, but not ideal for someone who grasps the math quickly and easily, and wants to really understand how things work.

Shankar is a little more difficult mathematically (and is thus often a poor introduction for an undergrad) but it very clearly lays out the assumptions being made, and how the math relates to the physics.

I haven't actually read the Sean Carroll book, but I took a course from him, and I can't imagine the book is anything but excellent.

Re:Some essentials (2, Informative)

Secret Rabbit (914973) | more than 5 years ago | (#25783221)

Griffiths QM book is absolutely terrible. All it does is skim the surface. Greiner is vastly superior. Griffiths E&M book is good though.

A survey of the best (3, Informative)

LaskoVortex (1153471) | more than 5 years ago | (#25782731)

Try Quantum Chemistry by McQuarrie for quantum theory--one of my favorites. It will get you up to speed on waves. I would have never thought there could be such a thing as a gentle introduction to the Schroedinger Equation, but McQuarrie is the closest there is. You can't go wrong with Atkins's Physical Chemistry for thermodynamics. For electrodynamics, there is Jackson. The classic on Information Theory is Cover and Thomas. For gravity, read Gravity (I've never read it though)--beware that its so thick, it has its own gravitational field. But I guess you don't mean relativistic physics. Decent Newtonian mechanics books are a dime a dozen because you don't need more than calculus to learn it.

My favorites (2, Informative)

physicsphairy (720718) | more than 5 years ago | (#25782739)

I think the best book for what you are asking (and I am 95% sure this is the right book, but I've lent it out so I had to look it up from dover) is "Vector Analysis" by Homer E. Nowell. It develops the theory of vector calculus using an intuitive approach and builds up the theory of electromagnetism simultaneously.

You might also look into the Feynman lectures. I do not normally recommend them as 'learning' material because, while excellent, I'm not aware that they come with any problem sets. But for you they may be a good supplement.

And, just to throw it out there, but it seems to me that most technical schools have enough overlap between physics degree requirements and math degree requirements that if you have a reasonable interest in the other it might not be out of the question to work that into your curriculum.

Man... (1)

NuclearError (1256172) | more than 5 years ago | (#25782741)

I'm in the exact opposite situation: I'm in a PDE class now with little grasp of the math but understand what they describe pretty well. I would hope you learn the material though, as I'd rather be able to get a solution from a mathematician. I don't know why you're snubbing undergrad books though - there are many that start to delve in the more advanced mathematics, enough so that it sets up the context for the PDEs. I'm a junior in nuclear engineering though - what's a 3rd year math PHD doing in PDE? Were you a Spanish major before? :)

Re:Man... (5, Funny)

JeanBaptiste (537955) | more than 5 years ago | (#25782791)

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

Re:Man... (1)

kayditty (641006) | more than 5 years ago | (#25783131)

for exceedingly strange definitions of "opposite," of course. if we are being that liberal with words, then, good sir, I, indeed, am in the exact opposite situation, and not you. I don't know anything about undergraduate level math or physics (well, perhaps this is also straining the definition for "undergraduate," given what is sometimes taught as undergraduate math in the US these days).

Yes, stick to the mathematics. (2, Insightful)

Swordfish (86310) | more than 5 years ago | (#25782743)

Seriously, the discussion of mathematical models in good PDE books is crisp and clear. The discussion in physics books is woolly and imprecise. That's because physicists rarely know enough mathematics to be able to express themselves precisely. So I would say: Just stick with the explanation of physical phenomena which you find in the mathematics books. It doesn't get much clearer than that, if you read the PDE books which I used to read.

Pick a different curriculum, seriously (0)

Anonymous Coward | more than 5 years ago | (#25782749)

If you're uncomfortable with PDE without Physics, then your curriculum is probably Mathematics and if you can't handle PDE, change majors, seriously. A Mathematics degree alone requires theoretical and abstract thinking to be successful. Seriously, find a Math counselor and talk to them about it. You'll never find any quick tutorial on Physics, unless of course you're Einstein or Newton.

Wave phenomena are complicated to begin with.... (1)

johnm1019 (1070174) | more than 5 years ago | (#25782751)

Having taken PDE's last year as a Nuke-E undergrad for intro to quantum, I can tell you that all the physical phenomena PDE's model are generally 'wave' based in _concept_. I also took our Physics 340 on "Heat Waves and Light" which is most of the stuff relevant to PDE's.... The textbook for that course was "Selected Chapters from 'University Physics', Young and Freedman, 11th edition." Where selected chapters were all the ones dealing with heat, waves, light, and a teeny bit of relativity. It's a pretty standard university physics textbook.

What? (3, Funny)

locokamil (850008) | more than 5 years ago | (#25782767)

Why are you taking partial differential equations as a graduate student?

Re:What? (3, Funny)

ari_j (90255) | more than 5 years ago | (#25782813)

Because his undergraduate degree is a B.A. in Political Science.

Re:What? (0)

Anonymous Coward | more than 5 years ago | (#25782845)

If i wasn't a coward, i would you you upmods. Clarification is necessary to determine what level of aptitude he has with maths in general.

Re:What? (0)

Anonymous Coward | more than 5 years ago | (#25782873)

There's a huge difference between the intro PDE class that undergrads usually take - and the more advanced ones that graduate students take. My concern is that he's a third year grad student...and is asking questions like this on slashdot when he should already know the answer.

Re:What? (0)

Anonymous Coward | more than 5 years ago | (#25782951)

Wow. That's a 3rd year undergrad course here in Canada. Are you guys that far behind?

Then again, we don't go outside much in the winter... ;)

Re:What? (4, Informative)

SleepingWaterBear (1152169) | more than 5 years ago | (#25782981)

Contrary to what most people seem to think, the material taught in most Calculus and Differential Equations courses has very little resemblance to what most Mathematicians study. These fields actually all fall under the heading of Analysis, which is just one of several major branches of mathematics. A student not interested in analysis could easily spend most of his math career working in another area.

For the most part, differential equations courses are aimed at non math majors, such as physicists, chemists, engineers, and the more analytically minded biologists and economists, so even a Math major specifically interested in analysis isn't necessarily going to take classes on partial differential equations.

I myself double majored in Physics and Math, and every single course i took about differential equations was for the Physics major rather than the math Major, so I think that Math grad student could quite easily end up with a PhD without ever dealing with differential equations unless they interested him.

Re:What? (1)

martin-boundary (547041) | more than 5 years ago | (#25783215)

Yes, but if he's in his 3rd PhD year and he missed all diff eqs courses up until now, then his research topic probably doesn't need it in the first place. He should be writing up at this stage.

Re:What? (3, Insightful)

Anonymous Coward | more than 5 years ago | (#25783239)

Wow, the level of ignorance here is astounding, that you would get moderated so highly. Real PDE (as mathematicians study it) is HARD, and requires a heavy background in analysis. This is not the same as undergrad "PDE" courses.

This is like the high schooler saying "Why are you taking algebra as an undergrad" to a math major studying abstract algebra. Its the same word and the topics are related, but its not even close to the same thing.

Simple... (0)

Anonymous Coward | more than 5 years ago | (#25782769)

Matter and Interactions by Chabay and Sherwood.

Why not a book for undergrads... (1, Interesting)

Anonymous Coward | more than 5 years ago | (#25782779)

When you are studying an undergraduate topic?

Some recommendations from another Math Ph.D (5, Insightful)

tehgnome (947555) | more than 5 years ago | (#25782785)

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 [] -for quantum theory and such use [] -for GR and such [] 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. []

Re:Some recommendations from another Math Ph.D (3, Interesting)

ari_j (90255) | more than 5 years ago | (#25782831)

Download Orbiter [] , launch a flight to Titan, and on the way there read the included PDFs regarding Dynamic state vector propagation and the like. Fewer pages, more direct and obvious application, etc.

Re:Some recommendations from another Math Ph.D (2, Informative)

TheEldest (913804) | more than 5 years ago | (#25782847)

Here's a good thermal book I used in my Undergrad. []

Also had a bit from []

It wasn't too bad.

Hard for me to say if either of those are really "good" texts as I hated Thermal.

Re:Some recommendations from another Math Ph.D (1)

darkmeridian (119044) | more than 5 years ago | (#25783113)

The OP is a graduate student in a field that isn't physics and says he never took physics anywhere. He's overestimating his abilities when he says he doesn't want to start with an undergraduate textbook because that's exactly where he should start. Unless he's cramming for an exam, he should take the time to start with college physics books and move up as he understands the material. PDE is difficult, but the basic physical concepts they represent are relatively simple to understand.

Re:Some recommendations from another Math Ph.D (3, Interesting)

Bemopolis (698691) | more than 5 years ago | (#25783127)

Jumping Jesus on a pogo stick, you're pointing him to The Black Death straight out of the gate? Why not give him underwear made of wolverine chow? Wheeler would have died ten years ago if not for the life-giving tears of those who opened that book unprepared. That is to say, everyone.

Seriously, dial it back a bit. First, hit the Feynman lectures (stop when you get to 'partons'.) Then, for someone coming from a mathematical bent, I'd suggest starting with Sokolnikoff's book "Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua", which covers a lot of ground besides GR. Due to the absence of a just and loving god it is out of print, but surely one of the profs in a math department with a PhD program has a copy (or at minimum the library.) And there's always copies on Alibris.

And, seconding suggestions from other posters, Kittel and Kroemer's "Thermal Physics" is a good starting point on thermo, As for quantum, in the absence of all knowledge in the field I'd start with Tipler's "Modern Physics", with the goal of ramping up to Cohen-Tannoudji, Diu, and Laloe's "Quantum Mechanics".

Seriously (0)

Anonymous Coward | more than 5 years ago | (#25782799)

How the f*ck could this be a legitimate question? I took PDE as an undergrad. How could a third year PHD student get that far without having had PDE already? I think my tensors are hurting.

Re:Seriously (1)

TheEldest (913804) | more than 5 years ago | (#25782879)

You're right. Because *everything* that a person needs to know about PDEs is taught in that undergrad class. This must be some sort of joke! The outrage!! We shall not stand for this!

Of course, the other option (even though it's completely ridiculous) is that--like most colleges--there is more than one level of PDE class, just as there is more than one calculus class. But I know, it's crazy (that's why we threw that out at the start!)

Re:Seriously (2, Insightful)

nomadic (141991) | more than 5 years ago | (#25782933)

Don't be too hard on them, the engineering majors never have to get into the really heavy math (they just think their math is heavy).

Re:Seriously (1)

Fujisawa Sensei (207127) | more than 5 years ago | (#25783157)

You're right. Because *everything* that a person needs to know about PDEs is taught in that undergrad class. This must be some sort of joke! The outrage!! We shall not stand for this!

Of course, the other option (even though it's completely ridiculous) is that--like most colleges--there is more than one level of PDE class, just as there is more than one calculus class. But I know, it's crazy (that's why we threw that out at the start!)

The material he is describing is what is covered in the undergrad PDE course. Its frequently given as both an undergrad course number and a graduate course number: same book, just more work for the grad level class.

not bitter (0)

Anonymous Coward | more than 5 years ago | (#25782809)

Not to sound bitter or anything, but you took a Ph.D. spot that a qualified student was rejected for.

The fact that you are even asking the question you asked, means you are nowhere near where you should be for *entry* into a Math Ph.D. program. It's a serious deficiency. not only to just be getting to PDE's, but to never have studied physics. How did you get a math undergrad without physics, and at what institution?

Physics/Astronomy Graduate student perspective (3, Informative)

hisperati (1408819) | more than 5 years ago | (#25782815)

Off the top of my head I would say... Introduction to Partial Differential Equations Applications - E. C. Zachmanoglou & Thoe; mostly math already, but has applications. For introduction to the wave equation try The Physics of Vibrations and Waves - Pain. The Shrodinger equation is explained well in Quantum Mechanics - Griffiths.

Enter the Physics vs. Math Holy War. (4, Funny)

ebbomega (410207) | more than 5 years ago | (#25782817)

I love watching this one happen.

It's funny because no matter what, the only thing a physicist and a mathematician has ever been able to agree on is magic mushrooms.

Road to reality (4, Informative)

jbolden (176878) | more than 5 years ago | (#25782821)

An excellent Physics book that is very math heavy but assumes no prereqs is Penrose's Road to Reality [] . This pretty much covers all of the main theory/formulas in cosmology, and he has 350 pages of math (much of it graduate level) to get there.

Juh what? (0)

Anonymous Coward | more than 5 years ago | (#25782827)

Yeah, what gives? PDEs, wave eqn/heat eqn are something third-year, undergraduate engineering students in canada have to learn.

This shouldn't be considered graduate-level stuff.

Try this book (1)

CEHT (164909) | more than 5 years ago | (#25782835)

When I was still in school, we use the Quantum Mechanics from Richard W. Robinett [] []

After that would be books on solid-state

The Feynman Lectures on Physics (4, Informative)

KonoWatakushi (910213) | more than 5 years ago | (#25782843)

I can not recommend these books enough. Feynman does a brilliant job of bringing the concepts of physics to life.

All together, they are quite extensive, but the individual topics are brief enough to digest in one sitting. Wether you only have a passing interest in physics, or a graduate degree in the field, you will find that there is much to appreciate in these lectures.

Even for those simply taking physics as requirement, I think that these would give you a real appreciation of the field, and probably make the classes a lot easier at that.

Re:The Feynman Lectures on Physics (1)

McSnarf (676600) | more than 5 years ago | (#25782979)

I second that recommendation.
They are the best set of general physics books you will fond - even if they are decades old.

(Mechanics are easy? Yes, until you reach friction, which isn't really understood.)

You'll have to like math, though. :)

Anon (0)

Anonymous Coward | more than 5 years ago | (#25782851)

Any quantum mechanics book.

Some random suggestions: (1)

physicistjedi (1408831) | more than 5 years ago | (#25782855)

* Thirring - Classical Mathematical Physics * Landau - The Classical Theory of Fields * Arnold - Mathematical Methods of Classical Mechanics * Sakurai - Modern Quantum Mechanics * Carroll - Spacetime and Geometry

Go to usenet (0)

Anonymous Coward | more than 5 years ago | (#25782859)


Watch for posts by someone named rockhound. The quantity and quality of the math and physics books are beyond all known philosophies!

They're All Targeted for Mathematicians (5, Informative)

w8dm4n (568583) | more than 5 years ago | (#25782863)

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):

    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.
    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.
    Rindler is the standard.
    Goldstein is pretty easy to find.
    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 [] 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,



i DO recommend an undergrad physics book... (1)

jonscilz (1135001) | more than 5 years ago | (#25782869)

as a recently graduated engineering student, and having taken my share of advanced calc and physics, i would actually recommend an undergrad physics book geared towards engineers. this is probably the best place to start in understanding how the equations you mentioned apply...

What I want to know is... (1)

Jane Q. Public (1010737) | more than 5 years ago | (#25782877)

... in what University can you get a Doctorate in Mathematics, without having taken any physics classes?

Part of the responsibility of a University is to see that you get a broad education. If you have had no physics, you do NOT have a broad education. Period.

Re:What I want to know is... (4, Funny)

HadouKen24 (989446) | more than 5 years ago | (#25783007)

Ooh, I like this game.

If you have never taken any psychology classes, you do NOT have a broad education. Period.

If you have never taken any philosophy classes, you do NOT have a broad education. Period.

If you have never taken any accounting classes, you do NOT have a broad education. Period.

This is fun!

Don't be an ass. Oops, sorry, too late... (2, Informative)

Jane Q. Public (1010737) | more than 5 years ago | (#25783163)

A 4- or 6-year degree in math or science should include both math and science. If not, you are NOT receiving the education you need to really understand your field. Regardless of how you feel, mathematics actually relates to (and is constrained by) our physical universe. If you do not understand that, then you are not well versed in either.

A degree in mathematics, from a responsible university, should include at least some physics. And of course a degree in physics requires a certain minimum of math, or you will not understand the subject.

What I was getting at is that it actually does work both ways. An understanding of our real world (physics), often constrains what real mathematicians do once they leave the university. You will not make it very far as an actuary, for example, if you do not understand at least the basic physics of what happens when someone experiences an automobile crash or a myocardial infarction.

Psychology adds to a broad education, but that is not even remotely related to what I was saying. Nor philosophy, nor accounting. I was not suggesting a educational free-for-all, just that physics and mathematics often go hand-in-hand.

I would not require it, but I do believe that it would benefit most people if they did have at least a little of each. I have. More than a little, actually.

But all that aside: math and physics are closely related "hard sciences". Philosophy, psychology, and accounting (we might as well include sociology and art history here), are all valuable education (at least I think they are), but they are NOT hard sciences, nor are they related to the subject at hand. In future, please stick to the matter under discussion.

Re:What I want to know is... (1)

egork (449605) | more than 5 years ago | (#25783275)

May be the parent is actually insightful without knowing it himself.
One has to take those three and a few others in addition to math and phys to have a broad education.

a few suggestions... (1)

krull (48492) | more than 5 years ago | (#25782885)

Since you want intuition, an introductory undergrad book might actually be a good idea. Higher level books will often assume you have seen the subject before.

Quantum Chemistry by McQuarrie is a good first book for quantum mechanics and the Schrodinger equation. Dirac's book is more advanced but also good (much harder to read). Much different focus though.

For electricity and magnetism a good first book is Griffiths Introduction to Electrodynamics. Here you'll see applications of the Poisson and Wave equations. Jackson is the classical "second" course textbook. (Upper level undergrad, beginning grad).

A good introduction to applications of the diffusion (i.e. heat) equation is Random Walks in Biology by Howard Berg. One benefit is that it is a very short book too!

For nonlinear equations there are too many references to know where to begin... There are millions of books on just the Navier-Stokes equations... Generally I'd just poke around Amazon and browse some of the books with good reviews.

Anyways if the original poster wants references for a specific PDE or area of physics please post a followup...

Mathematical Methods for Engineers and Scientists (0)

Anonymous Coward | more than 5 years ago | (#25782889)

There are three of them is the series and it is a little pricy but I have never seen anything explained this well. The author K.T. Tang has a constant named after him, an equation and an office at the Max Plank institute. He teaches at a small liberal arts school in tacoma, washington. I don't know why. But I was lucky enough to be given print offs of the book, for his class, before it was published.

Not to bring you down or anything, but.... (0, Flamebait)

zappepcs (820751) | more than 5 years ago | (#25782899)

I have not yet finished college.. forced to take night classes, and have no where near as much campus time/experience as you and many others have, but it only took me about ... oh, 20 seconds to Google for some good sites, and [] has links to pretty much all you mentioned. The links there point to other links for further reading. Note that in the reference section of wikipedia articles are links or information to books and such. I believe they're called citations. (citation needed)

As a third-year PhD math student.....

I'd think you would already have tried Google or Wikipedia. Your browser should have them on speed dial. So, really, what is your question?

BTW, Google has 916K hits for []

Not to rant, but why do people post 'ask Slashdot' questions that are so vague a 20 second search seems to answer them? Editors!!???

Re:Not to bring you down or anything, but.... (0)

Anonymous Coward | more than 5 years ago | (#25783073)

Do you have any idea how many books there are out there? We need guidance from people in the know as to which ones are the most suitable for us. This person's question was legitimate. Googling `Partial Differential Equations' is not the answer.

I'm sorry but, WHAT? (1)

richardkelleher (1184251) | more than 5 years ago | (#25782905)

What do you mean you are a third year PHD candidate in mathematics and you are only now taking PDE!? I took that sophomore year in my undergraduate engineering program, before we got into any of the serious engineering classes. If I remember correctly, it was the same time as we studied relativity in physics. What have you been doing all this time...

Re:I'm sorry but, WHAT? (1)

Singularitarian2048 (1068276) | more than 5 years ago | (#25783237)

Whatever it is you learned about PDEs as a sophomore undergrad engineering student, that wasn't the hard part.

Vector Analysis (2, Insightful)

thebrett (1408835) | more than 5 years ago | (#25782909)

is where to start when it comes to deriving PDEs. The heat equation and the wave equation fall easily out of vector analysis, as do a number of other familiar PDEs. I'd start with a vector analysis book.

The Feynman Lectures... (1)

sherifffruitfly (988148) | more than 5 years ago | (#25782917)

are of course a natural first place. For textbooks, it really doesn't matter all that much. At the level of generality you're operating in, textbooks are textbooks.

3rd year Math PHD and only NOW learnin Partial Dif (1)

Fallen Kell (165468) | more than 5 years ago | (#25782943)

My god, I had to learn that crap as a freshman UNDERGRAD!!! Now grant it I was an electrical/computer engineering major at the time, but still, I can't believe that a third year math PHD candidate would not have had partial diffs... I mean, seriously, it is the only way to do some stuff, especially anything in the real world (hence all the physics basis on the questions).

Re:3rd year Math PHD and only NOW learnin Partial (1)

McSnarf (676600) | more than 5 years ago | (#25783059)

The difference between engineering and math is that engineering focusses on real-world problems and the bit of math required to solve them. Because there are too many other things to learn - and engineering centers on practical applications. A lot of math appears to be intellectual masturbation unless you have proper training - and lacks any trivial practical application. Until suddenly, someone might find use for it to describe something in physics. Or not. A lot of the riddles you solve as a geek are applied math. Think topology.
Why would an engineer have to bother with abstract algebra? Or why should he be able to derive about everything in math from aimple set of axioms? :)

Engineers don't know math. Much.

(Disclaimer: Here speaks a CS guy who used to date a lovely Math PHD. And I thought MY mind was warped...)

Here are a few books (1, Informative)

Anonymous Coward | more than 5 years ago | (#25782949)

For classical mechanics you definitely want Goldstein. (

Another good supplement is The Variational Principles of Mechanics by Cornelius Lanczos of functional analysis fame (

For Electrodynamics, please partake of Griffiths. (

However, you will also want something on thermal physics and I have no awesome suggestions for that. But in classical mechanics you should get a lot of nice PDEs (such as the wave equation) which will be covered by the sources I mention. In electrodynamics you will get Laplace's equation (which will also show up in gravitation in classical mechanics). There are no really good books on QM that have been published, so I would just not worry about getting the physics behind the SchrÃdinger equation.

Spivak (1)

Hal-9001 (43188) | more than 5 years ago | (#25782995)

Many of the standard introductory undergraduate and graduate physics textbooks have been mentioned by other posters, but I'm surprised that no one has mentioned Michael Spivak's Elementary Mechanics from a Mathematician's Viewpoint [] , which is based on his Pathway Lectures at Keio University [] .

thermodynamics (1)

Khashishi (775369) | more than 5 years ago | (#25783017)

Many of the PDEs in physics are fairly simple.

The wave equation and diffusion equation are technically partial differential equations because of the 3 space dimensions and time, but these are simple PDEs because the three space dimensions are basically the same and the derivatives usually only appear as the Del operator, which treats each direction equally, and the boundary conditions are usually such that the constant of integration is just zero.

In thermodynamics, you actually have serious PDEs which involve variables that aren't all the same, and the constant of integration must be found by matching arbitrary functions to each other and boundary conditions.

This [] probably isn't a book for someone new to physics, but it does use some PDEs.

Good PDE book with relations to Physics (1)

SammoJG (1408843) | more than 5 years ago | (#25783019)

I am currently taking a pde course as an undergrad and am using Partial Differential Equations: An Introduction by Walter A. Strauss. While this book does have some faults it does an excellent job of relating pdes to their physical interpretation.

To all the people suggesting Griffiths QM.... (0)

Anonymous Coward | more than 5 years ago | (#25783041)

That book is terrible. He should have stopped after his masterpiece on Electrodynamics. Griffiths will simply not have enough math. To reiterate, Griffiths Quantum Mechanics book is bad, his Electrodynamics book is genius.

road to reality (1)

drago (1334) | more than 5 years ago | (#25783043)

I can recommend "The road to reality - a complete guide to the laws of the universe" by Roger Penrose. The guy undoubtedly knows what he's talking about (being a famous physician himself) and the book is very math-centric. First the mathematical concepts are explained, then based on that the physics of our universe.

Re:road to reality (2, Funny)

kayditty (641006) | more than 5 years ago | (#25783177)

you aren't the first person to ever call Roger Penrose a physician, but I think he probably deserves more credit than that. maybe I'm just an optimist.

Just to say... (1)

xhaju (1337031) | more than 5 years ago | (#25783151)

There are fabulous books by many different Russian authors called (mainly) "Equations of Mathematical Physics". They may help you...

The Big Book of Science (0)

Anonymous Coward | more than 5 years ago | (#25783171)

Yes, +1 to Science Stat here I come.

learning by applying (1)

bzipitidoo (647217) | more than 5 years ago | (#25783181)

I hope some math professors are reading this. They always seemed to think that they only needed to teach the "how", as "why" would already be obvious or would become clear. It didn't, not for me. More like that was the excuse, because actually "how" alone was much easier to teach. I studied PDEs in calculus classes, but never used them for anything. When they did come up with example uses, they were pretty contrived, and often could be solved with plain old algebra. Or they were so small that hand application of numerical methods could pin down the answer. Took only a few iterations of the Bisection method to get that zero, or you'd hack up a quick and dirty program to push some data into a linear algebra library function and get back results, something like that. And what's a student to think on hearing that although faster, Newton's Method, which is based on calculus, isn't as reliable as Bisection, which is simple algebra. Not good examples when trying to show students how useful and valuable calculus is.

Books? There's more than books alone out there. Lots of material on the web. Lots of combined material. Here are some books associated with Sage [] . Are you making use of mathematical software: Sage, Matlab, Mathematica, Maple, or some such? Or are you at least able to code up something in a general purpose language if needed? Much math is to the point where you can't advance without computers. Maybe I'm a bit behind. These days, I suppose all math students use such software.

I've noticed also that people with backgrounds in pure math don't have a good basic understanding of Computer Science. You know all about Fourier Transforms, you've heard of the Fast Fourier Transform, you've heard of big O, but you don't see what the big deal is about the FFT-- to you FFT is just one of many ways to do a Fourier Transform, one specific to computers which a person would not use if working out such a transform on paper. Do you have an appreciation of the algorithmic complexities of the math problems you are encountering? The way multiplication is done in grade school is just fine for relatively few small numbers, but when you want to do millions of multiplications of large numbers (1000 digits, say), you'd better use a computer, and you'd better program the computer to use FFT. A textbook on Numerical Methods could be worth checking out.

E&M (0)

Anonymous Coward | more than 5 years ago | (#25783285)

If you're curious about E&M, I suggest you look at Purcell's "Electricity and Magnetism". The book starts at a basic level (physics-wise, not math-wise) and works its way up.

You start with monopoles, derive the field from the inverse square law, move onto lines and sheets of charge, then dipoles, voltage & current, electronic circuits (resistors, capacitors, inductors, DC, AC, calculating V and I with diff eq, etc.).

Then you combine special relativity with the electric field and get...magnetism! Next you go through dipoles, electromagnetic radiation, induction, derive Maxwell's equations from scratch, and learn about how E&M fields interact with matter at the atomic through macroscopic scales.

The problems aren't your standard "Find X given Y using equation 5" problems. These actually make you think. Some examples off the top of my head:
-Find a resistor equivalent to an infinite repeating pattern of small resistors
-Prove that no magnetic field surrounds a torroidal electromagnet using Gauss's law
-Calculate the capacitance of two concentric hollow spheres

500 pages of physics and math. If you can understand half of it, you'll be well grounded. (No pun intended.)

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