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You should be "familiar" in the sense that you comprehend the content of the course. Many people have problems with analysis and the abstract nature of the topic. That's why grades matter, especially with regard to analysis. I said this on another thread, but analysis is the first course that really tells math professors whether a student has the potential to study math at a higher level (i.e. MA/PhD in math). Before that, everything is plug-&-chug.
gredow, the question is somewhat tough. The issue isn't whether or not you could do the material; it's whether or not the courses are offered. You could definitely do Calc 2-3 and linear algebra in two semesters (since 2 is an obvious pre-req for 3). That probably leaves analysis for the summer, and most schools probably won't teach it then (though you can find some, as this came up a few months ago on TM). The main problem you'll face with PhD admissions this year is that you'll only have grades for Calc 2 and maybe linear algebra, and many other applicants (at say top 30 or 40 schools) will have grades for more math courses. And the Stewart book you asked about on another thread is the one I used for Calc 1-3.
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