Mathematical Methods or Complex Analysis?

[djh101]

Hi, Physics Forums. I just have a quick question regarding which two math-type electives I should take as a physical chemistry major. Right now I am enrolled in Linear Algebra (Math 115A) and Mathematical Methods for Physicists (Physics 131) and plan on taking the second MM (Physics 132) next quarter. The first mathematical methods is mostly linear algebra with some Fourier series (see link) while the second is pretty much equivalent to Complex Analysis (Math 132).

What I was wondering is should I stick with my current plan or skip Mathematical Methods and take Complex Analysis now and Linear Algebra (115B) winter? So basically, I guess it's just Boas vs. Friedberg and Fisher.

http://www.registrar.ucla.edu/catalog/catalog13-14-654.htm
http://www.registrar.ucla.edu/catalog/catalog13-14-654.htm
http://www.math.ucla.edu/ugrad/courses/math132/index.shtml

 

[linda300]

As a physical chemist major you really don't need to take complex analysis at all, the other two classes are much more useful to you.

 

[djh101]

Well, it seems interesting (and it's listed as an approved elective for my major). In that case, would you recommend Mathematical Methods 1 with both Linear Algebra courses? My main concern is still whether MM will be useful or just redundant on top of Linear Algebra.

 

[linda300]

This is the right description for mathematical methods right?

Vectors and fields in space, linear transformations, matrices, and operators; Fourier series and integrals.

This is what I found after doing a search for linear algebra 115B, not sure if it's the right one but:

Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition.

Have you taken Linear algebra 115A?

It sounds like there is a much bigger overlap between 115A and mathematical methods compared to 115B. Also, 115B seems more relevant for a pure physics, in particular quantum physics, I'm not sure that is needed for physical chemistry, the most advanced mathematics we used in our undergraduate physical chemistry units was pretty basic group theory, and it was purely conceptual.

Have you taken these mathematics units?

135. Ordinary Differential Equations.
136. Partial Differential Equations.
142. Mathematical Modeling.

Of those I would say 135 would be the best one to have taken.

Back to your question, skipping mathematical methods means you will miss out on some vector calculus and Fourier series / integrals, which are pretty important tools. After having looked at all of the descriptions with more thought I think both 115B and Complex analysis may not be the best choices, even if you have already taken 115A I think mathematical methods would be a very useful class. But yea, I took a class identical to your complex analysis class and I have only ever really used Cauchy's theorem and power series, and I am doing my MSc in physics. Though it was cool to learn some of the neat integration methods possible with contours and residues.

The most useful mathematics unit I have ever taken is linear algebra (which is similar to your 115A) and ordinary differential equations (which is similar to your 135). Partial differential equations is also up there with the most useful units I've taken (136).

 

[djh101]

I will be taking 115A fall. The only other upper division math course I have taken so far is 134 (nonlinear differential equations). 136 is out of the question (only offered spring and I already have a pretty heavy load then), but I have Farlow's book and so far I think it's one of the best Dover books (pretty much designed for self teaching). So I guess 135 seems to be the winner (maybe I can even squeeze it in this quarter), although class planning tends to play like a game of Tetris so the ultimate deciding factor will probably be best schedule fit.

Anyway, excellent information. Thank you very much for your help.