Foundations of Analysis
by Joseph L. Taylor
Number of pages: 415
The course has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need when they move on to senior or graduate level mathematics courses. The second is to present a rigorous development of the calculus, beginning with a study of the properties of the real number system.
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by N. J. Lennes - John Wiley & Sons
This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions.
by Krzysztof Ciesielski - Heldermann Verlag
This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.
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 J. Hunter, B. Nachtergaele - World Scientific Publishing Company
Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required.