Real Analysis via Sequences and Series

Charles Little, Kee L. Teo, Bruce van Brunt (Autoren)

Buch | Hardcover

476 Seiten

2015
Springer-Verlag New York Inc.
978-1-4939-2650-3 (ISBN)

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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.

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

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.

Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	27 Illustrations, black and white; XI, 476 p. 27 illus.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Airy function • Airy's equation • Baire's theorem • Bolzano-Weierstrass theorem • Cartesian Product • Cauchy condensation test • Dirichlet's test • infinite series • integral test • Kummer-Jensen test • limits of functions • real analysis text adoption • Riemann integral • sequence convergence • sequences
ISBN-10	1-4939-2650-0 / 1493926500
ISBN-13	978-1-4939-2650-3 / 9781493926503
Zustand	Neuware