Real Analysis via Sequences and Series

Charles Little, Teo Kee and Bruce van Brunt are professors of Mathematics at Massey University in New Zealand.

"The list of main topics covered is quite standard: sequences, series, limits, continuity, differentiation, Riemann integration, uniform convergence ... . This is a well-written textbook with an abundance of worked examples and exercises that is intended for a first course in analysis with modest ambitions." (Brian S. Thomson, Mathematical Reviews, March, 2016) "The authors ... introduce sequences and series at the beginning and build the fundamental concepts of analysis from them. ... it achieves the same goal of introducing students to mathematical rigor and basic concepts and results in real analysis. ... Summing Up: Recommended. Upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 53 (5), January, 2016) "This textbook is based on the central idea that concepts such as continuity, differentiation and integration are approached via the concepts of sequences and series. ... Most of the sections are followed by exercises. The textbook is recommended for a first course in mathematical analysis." (Sorin Gheorghe Gal, zbMATH, Vol. 1325.26002, 2016)

• Preface.- 1. Introduction.- 2. Sequences.- 3. Series.- 4. Limits of Functions.- 5. Continuity.- 6. Differentiability.- 7. The Riemann Integral.- 8. Taylor Polynomials and Taylor Series.- 9. The Fixed Point Problem.- 10. Sequences of Functions.- Bibliography.- Index.