Real Analysis via Sequences and Series

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

ISBN 10: 149394181X / ISBN 13: 9781493941810

Editore: Springer-Verlag New York Inc., US, 2016

Riguardo questo articolo

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 ? and e and a treatment of Newton's method as a special instance of finding fixed points of iterated functions. Softcover reprint of the original 1st ed. 2015.

Codice articolo LU-9781493941810

Dati bibliografici

• Titolo: Real Analysis via Sequences and Series
• Editore: Springer-Verlag New York Inc., US
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 149394181X
• ISBN 13: 9781493941810
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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