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Real Analysis via Sequences and Series - Charles Little, Kee L. Teo, Bruce van Brunt

Real Analysis via Sequences and Series

Buch | Hardcover
476 Seiten
2015
Springer-Verlag New York Inc.
978-1-4939-2650-3 (ISBN)
CHF 104,80 inkl. MwSt
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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
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