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 William F. Trench - Prentice Hall
This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging concepts as clearly as possible. Written for those who want to gain an understanding of mathematical analysis and challenging concepts.
by Dan Sloughter - Synechism.org
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, the author is assuming that the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses.
by W W L Chen - Macquarie University
An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc.
by G. H. Hardy - Cambridge University Press
The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems.