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I am looking for a book on (one variable) real analysis that includes, simultaneously:

  • A treatment of the abstract and theoretical aspects of real analysis;
  • A treatment of the more mechanical and computational aspects of calculus (such as techniques of antidifferentiation, for instance).

The reason I'm finding this hard to find is that usually undergraduates take a course in calculus where they learn mostly the mechanics and then take a real analysis course where the emphasis is on theory. I'm looking for a book that integrates these two aspects. Ideally the logical prerequisites should be (besides some mathematical maturity) the mathematics one learns in high school (algebra, trigonometry, ...).

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    @LeonidKovalev: Thank you for the suggestion, I have looked at the table of contents in the first volume and it seems to correspond to what I had in mind.2012-07-30

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