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, ...).