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So far, I know how to differentiate, limits and a few other things.

At my college the teacher is talking about fundamental sequences, Cauchy, Raabe-Duhamel, D'Alembert, general criteria of convergence, Weierstrass...

Where can I start to really understand these topics well? Maybe a book or something? (Hint: I don't like those books with plenty of formulas and no practical examples).

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Any introductory real analysis text should do. But be sure it's a "baby analysis" text, such as – David Mitra Nov 19 '11 at 10:35
On the web, is a good place to start. – David Mitra Nov 19 '11 at 10:41
What does "s.o." in your title mean? – Byron Schmuland Nov 19 '11 at 15:50
@ByronSchmuland so on – Andrew Nov 19 '11 at 16:29
up vote 0 down vote accepted

LOTS of terrific real analysis textbooks out there,but it sounds to me like you want something with just the basics and lots of examples. There's no better book for that then Kenneth Ross' Elementary Analysis:The Theory Of Calculus. It's exactly what the title says it is and it's by a master analyst.There's no better book for a student beginning real analysis with a weak calculus background who needs to get up to speed, which sadly is all too common these days. Another book you could try which is very good for this,but considerably more difficult, is Michael Spivak's classic Calculus. Don't let the title fool you-this is a rigorous presentation of calculus with thorough discussions of convergence and limits. As I said,though-it's considerably harder then Ross,especially the exercises.

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Thanks a lot, I will start with the first one. – Andrew Nov 19 '11 at 16:31

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