Real Analysis via Sequences and Series (eBook)

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

eBook Download: PDF

2015 | 2015
XI, 476 Seiten
Springer New York (Verlag)
978-1-4939-2651-0 (ISBN)

Infos

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

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

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 28.5.2015
• Reihe/Serie: Undergraduate Texts in Mathematics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• 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: 1-4939-2651-9 / 1493926519
• ISBN-13: 978-1-4939-2651-0 / 9781493926510