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...
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...