Where should I go after Boas' Mathematical Methods in Physics?

[physics16]

I'm currently a rising sophomore (undergrad), and I'm trying to fill in some gaps in my applied math background this summer. So far, I've taken linear algebra and multi/intro analysis, but they were both theory-only and had very few applications (ex: I finished LA without knowing the various methods of diagonalizing or inverting a given matrix). I just finished going through Boas' text, but I feel like I need something a little more condensed (only bits and pieces of about 1/3 of the chapters I hadn't seen before). Any recommendations? (For next year I'm looking at QM, stat mech, and possibly GR)

Also, is self-studying texts the best way to be going about this? I would really prefer saving an elective spot for pure math rather than a mathematical methods in physics course.

 

[Vanadium 50]

Can you work any problem in Boas cold? Stick your finger in the book and work the nearest problem?

 

[ZapperZ]

I'm currently a rising sophomore (undergrad), and I'm trying to fill in some gaps in my applied math background this summer. So far, I've taken linear algebra and multi/intro analysis, but they were both theory-only and had very few applications (ex: I finished LA without knowing the various methods of diagonalizing or inverting a given matrix). I just finished going through Boas' text, but I feel like I need something a little more condensed (only bits and pieces of about 1/3 of the chapters I hadn't seen before). Any recommendations? (For next year I'm looking at QM, stat mech, and possibly GR)

I don't quite understand this. What exactly do you mean by "... I've just finished going through Boas' text..."? Did you work through all the problems in that text?

You claim to have done linear algebra by "... theory only..." and "... without knowing ...diagonalization...". But you have "gone through" Boas? She covered both applications and diagonalization in linear algebra. Did you go through those? Have you mastered it?

This is a head-scratcher.

Zz.

 

[physics16]

Sorry for the ambiguity. By "go through" I meant that I skimmed through portions I was familiar with, read the sections I wasn't, and then worked on the exercises I thought I couldn't do/looked interesting. Could I do any problem cold? No. I'd have to look up the special functions in chapters 11 and 12, but anything else is fair game. In general, my confidence in solving the problems still depends on whether I've been using the techniques in physics throughout the semester (ex: I know Rodrigues' Formula by heart; I'd be a little more pressed to come up with a Bessel function).

@ZapperZ: I read Boas' text after my linear algebra course, so yes, I was able to fill in that particularly glaring hole.

 

[Vanadium 50]

If you can't work every problem, it's probably too soon to move on.

 

[alan2]

Personally, I think that math is sorely lacking in undergrad physics programs, at least in the US. I suggest you get some good "math for scientists and engineers" books. These are my favorites, I still have old editions of them all on my shelf and refer to them after 20 or so years:

https://www.amazon.com/dp/0471154962/?tag=pfamazon01-20

https://www.amazon.com/dp/0130111899/?tag=pfamazon01-20

https://www.amazon.com/dp/0486492796/?tag=pfamazon01-20

https://www.amazon.com/dp/0133214311/?tag=pfamazon01-20

Personally, I think that you should know everything in these books (or know where to find it when you need it) by the time you graduate. We had to take courses in complex variables, boundary value problems, and vector analysis through the math dept as requirements for the BS in physics but now it seems that they want to cram it all into a methods course in the physics dept. I don't know how you can understand or become proficient in anything by taking a course with a book like Boas. If you have any plans to go to grad school you'll want to be proficient at math.

 

[Fusiontron]

https://www.amazon.com/dp/0521679710/?tag=pfamazon01-20

I like this book. It's similar to Boas but more verbose.

 

[Jorriss]

The ultimate (in my opinion) mathematical methods book is Bender & Orszag. If you are as comfortable with Boas as you suggest you should find the text manageable.

If you want a text like Boas 2.0 there is always Arfken & Weber, Byron & Fuller, Hassani, etc. Take your pick.

If you want a more focused textbook, for example, say you want to focus on PDES, a text such as Strauss is well oriented for physics. This is not quite what you asked for but if you want to start learning differential geometry (which may or may not be useful depending on your inclinations) a textbook like Do Carmo Differential geometry of curves and surfaces is a pretty good choice too.

 

[alan2]

I agree with Fusiontron, I forgot about that book. It's probably the most complete at your level. I wouldn't even begin to read Bender until you've mastered everything at your level. It's more advanced, mainly asymptotics and advanced perturbation techniques.