Where to go next? did the intro to analysis

[octol]

Ok I've done an introductary course in analysis using the first 2/3 of Parzynski and Zipse - Introduction to Mathematical Analysis. This (I think) is about equivalent to Rudin up and including chap 7 (series of functions).

I probably won't have time to take any more classes in mathematics as I'm more of a theoretical physicist, but I'd still try to advance my knowledge in analysis a bit on my own. The problem is I don't know in which direction I should continue.

So far I'm considering one of the following options:

1) Fleming - Functions of Several Variables

2) Kreyzig - Introductory Functional analysis

3) Spivak - Calculus on Manifolds

The criteria is that it can't be too big a step up as I'm not a mathematician and I'll be studying on my own. Kreyzig looks very nice from that aspect, while Spivak seems scary.

Anybody has any suggestions?

 

[George Jones]

I have all of the books that you listed as options, but I have none of them with me right now.

It might be useful to study, in some book, the material in chapter 9 of Blue Rudin. This stuff is probably covered in both Fleming and Spivak. Even though Spivak is a wonderful book, Fleming's treatment is probably more accessible.

Kreyzig was the text for a course that I took, and I think it would make a great self-study text. Studying Kreyzig would give you a good grounding (Better than many physicsts receive!) in the mathematics that underlies quantum theory.

 

[octol]

Thanks for the help. So I will probably start by reading Kreyszig, it doesn't seem as scary as the others. At least one day I hope I'll be able to master the book by Spivak, but that day seems far away...