by Martin Smith-Martinez, et al.
Publisher: Wikibooks 2013
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.
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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 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.
by Elias Zakon - The Trillia Group
Topics include metric spaces, convergent sequences, open and closed sets, function limits and continuity, sequences and series of functions, compact sets, power series, Taylor's theorem, differentiation and integration, total variation, and more.
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.