Real Analysis via Sequences and Series
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 p and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
| Autor: | Little, Charles H.C. Teo, Kee L. van Brunt, Bruce |
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| ISBN: | 9781493926503 |
| Sprache: | Englisch |
| Seitenzahl: | 476 |
| Produktart: | Gebunden |
| Verlag: | Springer US |
| Veröffentlicht: | 29.05.2015 |
| Schlagworte: | Airy's equation Airy function Baire's theorem Bolzano-Weierstrass theorem Cartesian product Cauchy condensation test Dirichlet's test Kummer-Jensen test Riemann integral Sequences |
Charles Little, Teo Kee and Bruce van Brunt are professors of Mathematics at Massey University in New Zealand.