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Textbook: if deep, then Zorich.
You will experience all the pain of a matan on yourself
I studied Fichtenholtz. Good tutorial and explains everything clearly
Of the problem books, Berman's "Collection of Problems in the Course of Mathematical Analysis" is also good (it's strange that no one wrote it). It even has a book with detailed solutions to some problems.
Their good ones, who have not yet appeared here:
U. Rudin. Fundamentals of mathematical analysis. M .: Mir, 1976.
The level of TS is unknown, so it is difficult to advise anything specific. And the aims of the study are not formulated.
Fundamentals of mathematical analysis. In 2 hours Ilyin V.A., Poznyak E.G. - a good duplex. Good explanations for the evidence. All topics are covered in detail.
And with Demidovich, the main thing is not to miss. There are for higher education institutions and there are for universities. The first task is much easier. It is better to study according to the problem book for universities.
More to understand everything that happens in the mat. this book helps with the analysis .
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