How We Got From There to Here: A Story of Real Analysis
by Robert Rogers, Eugene Boman
Publisher: Open SUNY Textbooks 2013
Number of pages: 210
This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments.
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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.
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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.
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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.