Real Analysis via Sequences and Series, Springer (2015) torrent

Charles H.C. Little, Kee L. Teo, Bruce van Brunt (auth.)-Real Analysis via Sequences and Series-Springer-Verlag New York (2015)


This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.



Series: Undergraduate Texts in Mathematics
Hardcover: 476 pages
Publisher: Springer; 2015 edition (May 29, 2015)
Language: English
ISBN-10: 1493926500
ISBN-13: 978-1493926503