Reddit mentions of Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics)

You might like Hassani 1 better (or more readable) compared to Boas (Boas has more problems though). Though I'm not suggesting it as a preparation for your test next week (although you never know; you might pick it up from the library tomorrow and find out it answered many of your questions). It's one of the books that you shouldn't rush through (a whole summer working through it, solving 70-80% of the problems, would be a good idea).

Bra Ket notation shouldn't be too difficult if you've taken 'linear algebra' already (again Hassani has a few chapters on LA, but I used Leon when I took LA class). Schmidt ortho is covered in an LA class (again also is in Hassani).

Other stuff you mentioned seem like special topics in Diff. Eq, save for Complex Fourier which should be under 'complex analysis' I guess.

I hope this helps FWIW.

That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)

• Griffiths (the standard first course, and maybe the best one)
  
• Cohen-Tannoudji (another good one, similar to Griffiths and a bit more thorough)
  
• Shankar (sometimes used as a first course, sometimes used as graduate text; unless you are really good at linear algebra, you'd get more out of starting with the first two books instead of Shankar)
  
  By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&ie=UTF8&qid=1372650839&sr=1-1&keywords=classical+mechanics)
  
  
  Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of
  
  
• Paul's Free Online Notes (the stuff after calculus, but without some of the specialized ways physicists use the material)
  
• Boas (the standard, focuses on problem-solving recipes)
  
• Nearing (very similar to Boas, but free and online!)
  
• Little Hassani (Boas done right, with all the recipes plus real explanations of the math behind them; after my math methods class taught from Boas, I immediately sold Boas and bought this with no regrets)
  
  When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out
  
  
• Sakurai (the standard graduate QM book; any of the other three QM texts will prepare you for this one, and this one will prepare you for your PhD qualifying exams)
  
• Big Hassani(this isn't just the tools used in theoretical physics, it's the content of mathematical physics. This is one of two math-for-physics books that I keep at my desk when I do my research, and the other is Little Hassani)
  
• Peskin and Schroeder (the standard book on quantum field theory, the relativistic quantum theory of particles and fields; either Sakurai or Shankar will prepare you for this)
  
  Aside from the above, the most relevant free online sources at this level are
  
  
• Khan Academy
  
• Leonard Susskind's Modern Physics lectures
  
• MIT's Open CourseWare

you can look at Cahill and Arfken et al (older edition) online, and a few others:

http://www.scribd.com/doc/91670553/Arfken-Math-Physics

http://www.goldbart.gatech.edu/PG_MS_MfP.htm

http://books.google.com/books/about/Physical_Mathematics.html?id=13YeX-SXkWYC

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hassani also gets good reviews http://www.amazon.com/Mathematical-Methods-Students-Physics-Related/dp/0387095039/