Introduction to real analysis 4th ed R. Bartle, D. Sherbert-wiley-2011,
Chapter 1 has a brief summary of the notions and notations for sets and functions that will be used.
Chapter 2 presents the properties of the real number system.
In Chapter 3, a thorough treatment of sequences is given, along with the associated limit concepts. The material is of the greatest importance.
Chapter 4 on limits of functions and Chapter 5 on continuous functions constitute the heart of the book.
The basic theory of the derivative is given in the first part of Chapter 6.
In Chapter 7, the Riemann integral is defined in Section 7.1 as a limit of Riemann sums.
Sequences offunctions and uniform convergence are discussed in the first twosections of Chapter 8, Chapters 8 and 9 are intrinsically important, and they also show how the material in the earlier chapters can be applied.
Chapter 10 is a presentation of thegeneralized Riemann integral. Chapter 11 deals with topological concepts
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