Basic Analysis: Introduction to Real Analysis
by Jiri Lebl
Publisher: Lulu.com 2009
Number of pages: 161
This free online textbook is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A prerequisite for the course is a basic proof course. The text does not cover topics such as metric spaces, which a more advanced text would.
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by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.
by B. S. Thomson, J. B. Bruckner, A. M. Bruckner - Prentice Hall
The book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the big picture and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory and other.
by Bruce K. Driver - Springer
These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.
by Elias Zakon - The TrilliaGroup
This book follows the release of the author's Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses. The text is appropriate for any second course in real analysis or mathematical analysis.