Math Major Finds Physics - ODEs, PDEs, Vector Calc, LA

[glebovg]

Which Physics courses would interest a Math major? I did not like Classical Mechanics. I really like ODEs, PDEs, Vector Calculus, Linear Algebra, etc.

 

[Lavabug]

Was this classical mechanics a la Newton or did you study analytical mechanics(Hamilton-Jacobi theory, small oscillations, etc)? You might like that more.

Certainly electromagnetism if you like vector calculus and introductory QM, at least in my course we've been touching upon all of our knowledge from linear algebra, calculus and ode's from day 1.

 

[nonequilibrium]

A decent electromagnetism course, fo sho.

 

[glebovg]

Yes, it was mostly Newtonian Mechanics. I was considering QM. I need Intro to Modern Physics to take QM. Do you think I will find it interesting? How about Thermodynamics and Statistical Mechanics? Even after taking Calc I, II, II, ODEs, and Linear Algebra, I still found Newtonian Mechanics confusing. Is physics like this in general i.e. do you have to think in a different way? For example, I am taking Intro to Dynamical Systems and I think it is interesting but I find it extremely confusing.

 

[chiro]

Which Physics courses would interest a Math major? I did not like Classical Mechanics. I really like ODEs, PDEs, Vector Calculus, Linear Algebra, etc.

If your department offer a fluid mechanics course to math/physics majors (and not just engineering), that might be up your alley.

 

[Lavabug]

I agree with chiro but at least at my university, my fluid mechanics course makes quite a bit of use of thermodynamics and some EM (astrophysical applications), which I presume you haven't taken.

I'd get a firm grasp on Newtonian mechanics before taking anything else though, what did you find confusing? Everything else you will study in EM, thermodynamics, fluid mechanics and even QM will base itself on it. All you really need to understand it is geometry/vector algebra and some calculus for the more rigorous parts, but you've taken your calculus and ODE's so I really don't see what's the problem.

 

[Mépris]

Glebovg - yeah, I guess you're pretty much "doomed" to think in a "different way". You really have to be very familiar with all the theorems/concepts/laws. You have to understand the particularly system you're dealing with.

Say, you're doing a problem with two masses, m1 & m2, connected on the same string (assume there's no friction), passing over a pulley. I find it useful to do this on a "case by case" basis. First, I look at the problem from the perspective of m1. What are the forces acting on it? There's the tension in the string - great! What else? Is m1 heavier than m2? Yes? So:

[(m1)x(g)] - T = (m1)(a)

Where, g = acceleration due to gravity, T = Tension of the string, a = resultant acceleration.

I then proceed to do the same with m2 and from there, I find the missing variable I had to find! It's not very complicated, although it can be quite confusing at first. It's a "different" kind of problem solving than what you'd typically be doing in math, I suppose.

 

[glebovg]

Should I take Thermodynamics & Statistical Mechanics and Intro to Modern Physics?

Mépris - What I find confusing are geometrical arguments and the way you are supposed to reason in mechanics and perhaps in physics in general. In Intro to Dynamical Systems, which is a Math course we analyze systems case by case e.g. what happens when the parameter, say μ changes (i.e. μ > 1, μ < 1, μ = 1), what is the critical value of the parameter at which bifurcation occurs, what happens when, say ε << 1, or t → ∞ etc. I find this confusing.

 

[glebovg]

What are the most essential physics courses for applied math?

 

[chiro]

What are the most essential physics courses for applied math?

It depends what kind of applied math you want to do. Have you narrowed down your choices to a specific list of courses?

 

[cbetanco]

If you like vector calculus and PDEs, then I would say electrodynamics (not first year level, more like 3rd year physics major level) would be the way to go. It makes heavy use of vector calculus.

If you really want a mix of PDEs, ODEs, vector calculus and a little bit more weight given to Linear Algebra, I would say Quantum mechanics is a good class (I didn't really appreciate linear algebra until I took QM).

But both of these courses will require you to have some familiarity with classical mechanics. Especially QM, you will need to at least know what the Hamiltonian is at least. I would skip modern physics if you want a class that is heavier on the math.

 

[Mépris]

^
Theoretically, would it be possible for a math/applied math major to double major in Physics without beefing up their time table too much? That is, only taking the "Senior" variant of the courses. Am I correct in assuming that the only difference between the senior physics courses and their sophomore counterparts is mathematical content?

 

[glebovg]

Do you think Thermodynamics and Statistical Mechanics would be hard for a math major to grasp?

 

[nlsherrill]

Do you think Thermodynamics and Statistical Mechanics would be hard for a math major to grasp?

If you thought Newtonian mechanics was confusing, then stat. mech would probably be a nightmare. It doesn't have anything to do with you being a math major or not.

 

[glebovg]

Of course Newtonian mechanics is confusing. Newtonian mechanics is factually incorrect, because it fails to take into account relativity and quantum mechanics, but it can be used as an approximation in many situations.

 

[nonequilibrium]

Ha, if you think that would make Newtonian mechanics more confusing than QM and relativity, you're in for a surprise... Newtonian mechanics is actually the least confusing physics, because it comes closest to our intuition.

That being said, statistical mechanics is, according to me, not more confusing than Newton. It's a very mathematical and conceptually clear branch of physics. I warmly suggest it to all.

(Thermodynamics I like less; it's very practical but not conceptually clear. In effect, statistical mechanics is the derivation of thermodynamics using Newtonian concepts.)

 

[Cuauhtemoc]

Is that course the same? I mean, it's statistical mechanics together with thermodynamics?
Because it may ask for some previous knowledge of thermodynamics. If not, if it derives everything from scratch than you will probably like it.