What subject area should I focus on during my six months off from college?

[robertm]

Due to my circumstances I will soon have a significant block of time out of college(6 months or so). I have so far finished my first year of undergraduate studies and have taken trig., calculus I, introductory physics, mechanics, and the other common first year required courses. I work well studying independently, and have been doing so for several years in order to get ahead (which has worked out quite well for me). I am working towards a Physics degree and/or Applied Mathematics degree (that's a whole different issue).

Anyway, this time off I will be having will be spent working part time, wandering through the woods, and hopefully getting some serious studying done. My question is in regard to what subject area I should focus my efforts on.

I tend to do best by intensely but narrowly focusing on a particular subject, rather than focusing more broadly and generally in several areas. My initial thoughts are to delve much more deeply and thoroughly into calculus, as I feel I am significantly more well prepared for my second and third year physics courses than the more advanced mathematics.

So what do you think? I've got six months of stress free learning opportunity that I do not want to waste.

 

[robertm]

O.k., so I guess my post was to loquacious.

Tl;dr: I have about 6 months of free time to prepare for my second year of undergraduate studies (physics or applied mathematics with a minor in physics). What do you think I should focus on?

 

[naele]

You could get Pollard and Tenenbaum's book on ordinary differential equations. There's a loooooooot of material in there. Alternatively, get yourself Boas math methods book and learn complex contour integration and the residue theorem. Then go over integral transforms, Fourier and Laplace, and finish off with Green's function for ODE and PDEs.

 

[BogMonkey]

I recommend studying what you feel like studying at the time. The more interested you are in what your learning the quicker you'll absorb it. In that space of time you could easily cover the whole second year calculus material as well as get a huge head start in any physics your course will cover.

 

[robertm]

naele: Thanks very much for the specifics, quite helpful. My copy of Mathematical Methods in the Physical Sciences has been in the mail for a while now and should be arriving shortly. I'll definitely look into Pollard & Tenenbaum. The text I'm working out of now is Salas, Hille, & Etgen Calculus One and Several Variables.

BogMonkey: Thanks for the encouragement; that is indeed what I hope I can accomplish. I'm already fairly far along as far as my upcoming physics courses are concerned, so I should have plenty of time to work on my maths.

It certainly is a major benefit for me (grade-wise) to learn and understand the material well, before I even attend the class, however my main goal is of course to fully understand and master the subjects that are of interest to me. I suppose as I dig more deeply into the subject matter, I will get a better idea as to the proper course of action that will leave me with the maximum of comprehension and the minimum of frustration.

In any case, seeing as most of my time off will be through spring and summer, I will be doing as much of my work outside in the sun as is possible!