A Primer of Real Analysis
by Dan Sloughter
Publisher: Synechism.org 2009
Number of pages: 152
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses and has had some exposure to the ideas of mathematical proof.
Home page url
Download or read it online for free here:
by Pierre Schapira - Université Paris VI
The notes provide a short presentation of the main concepts of differential calculus. Our point of view is the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis.
by Charles Walmsley - Cambridge University Press
Originally published in 1926, this text was aimed at first-year undergraduates studying physics and chemistry, to help them become acquainted with the concepts and processes of differentiation and integration. A prominence is given to inequalities.
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 Lee Larson - University of Louisville
From the table of contents: Basic Ideas (Sets, Functions and Relations, Cardinality); The Real Numbers; Sequences; Series; The Topology of R; Limits of Functions; Differentiation; Integration; Sequences of Functions; Fourier Series.