Physical Chemistry Electives: ODE, Mechanics, or Mathematical Methods?

[djh101]

Hello, everyone. I am currently a junior [physical] chemistry major and am picking out my future upper division electives. I've narrowed them down to a handful of classes and what I'm looking for is just a little background information on them, which ones might be better than others, general advice, etc.

-Linear and Nonlinear Systems of Differential Equations (Math 134, currently enrolled)
-Ordinary Differential Equations (Math 135)
-Partial Differential Equations (Math 136)
-Analytical Mechanics I (Physics 105A)
-Analytical Mechanics II (Physics 105B)
-Mathematical Methods of Physics I (Physics 131)
-Mathematical Methods of Physics II (Physics 132)

Course Descriptions:
Physics: http://www.registrar.ucla.edu/catalog/catalog12-13-667.htm
Math: http://www.registrar.ucla.edu/schedule/catalog.aspx?sa=MATH+++&funsel=3

 

[Jorriss]

Analytical mechanics and mathematical methods are both very important to physical chemistry.

Is it possible to make both?

 

[djh101]

I need six electives, so I can take most of these (all but 1 or 2, probably), more or less depending on whether I overload my schedule and graduate on time or take an extra quarter (in which case I'd like to take quantum mechanics and thermodynamics, which are only offered in fall), so I guess a better question than what to take would be what not to take.

Right now I'm leaning towards dropping ODE first, since it has multiple overlaps with mathematical methods (fourier, laplace) (and I think PDE and L&NDE will be plenty of fun by themselves).

 

[Jorriss]

At first I was going to say ODEs is the least important but the course description of it sure sounds pretty good.

Can't really go wrong with any of those courses but if I were in your position I would take analytical mechanics and math methods still, if I could only pick that amount.

 

[djh101]

Alright, thank you very much. Physics 132 (mathematical methods II) seems like an interesting class, but it's not actually a prerequisite for anything or even a requirement for physics majors. Do you think you could give any additional details about its contents (where it might be used and what not)?

Description:
Functions of a complex variable, including Riemann surfaces, analytic functions, Cauchy theorem and formula, Taylor and Laurent series, calculus of residues, and Laplace transforms.

 

[Jorriss]

Not sure what kind of details I could give.

In terms of the course, or how those topics are used in physical chemistry?

 

[djh101]

Just a little bit about where the topics come up in physical chemistry (or in general).

 

[Jorriss]

Just a little bit about where the topics come up in physical chemistry (or in general).

It's hard to give a very concise break down since complex analysis shows up so much in the physical sciences.

The residue theorem is useful for solving large classes of integrals that show up in quantum mechanics.

Branch cuts are used to make multivalued functions single valued. This is useful to know for numerical purposes as often times a particular branch cut is more computationally efficient than another but, say, mathematica has a preset branch cut you need to know how to express a certain cut in terms of another.

In the class you'll probably learn the Kramers-Kronig relations which are very important to issues of causality. This showed up this quarter in statistical mechanics when discussing dielectric relaxation.

Laplace transforms are a very useful technique for solving differential and integral equations (among other reasons). As an aside, unlike the Fourier transform, the inverse laplace transform is more complicated than the forward laplace transform and it would be useful to see this in a class I'd wager.

Plus, not to mention, many phenomena are inherently complex valued functions and you should be well versed in complex algebra and calculus just to be able to manipulate expressions.

 

[djh101]

Interesting. Well, thank you, very much. I look forward to my future physics electives.