Elementary Real Analysis
by B. S. Thomson, J. B. Bruckner, A. M. Bruckner
Publisher: Prentice Hall 2001
Number of pages: 735
Elementary Real Analysis 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, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis.
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by Marcel B. Finan - Arkansas Tech University
The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty.
by Juha Heinonen
In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. From the table of contents: Introduction; Extension; Differentiability; Sobolev spaces; Whitney flat forms; Locally standard Lipschitz structures.
by Martin Smith-Martinez, et al. - Wikibooks
This introductory book is concerned in particular with analysis in the context of the real numbers. It will first develop the basic concepts needed for the idea of functions, then move on to the more analysis-based topics.
by Shlomo Sternberg
The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.