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Real Analysis: A First Course by Russell Gordon (Paperback, 2002)

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Appendices review essential ideas of mathematical logic, sets and function. Limits and Continuity. The Limit of a Function. Continuous Functions. Uniform Continuity. Monotone Functions. Introductory material, such as the study of sets, functions, relations, and mathematical induction has been kept to a minimum and is presented in context for students to acquire a working knowledge.

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Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical methods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.