Kenneth A. Ross

Elementary Analysis (eBook, PDF)

The Theory of Calculus

• Format: PDF

Produktbeschreibung

Designed for students having no previous experience with rigorous proofs, this text on analysis is intended to follow a standard calculus course. It will be useful for students planning to continue in mathematics (with, for example, complex variables, differential equations, numerical analysis, multivariable calculus, or statistics), as well as for future secondary school teachers.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 264
• Erscheinungstermin: 17. April 2013
• Englisch
• ISBN-13: 9781475739718
• Artikelnr.: 44054089

Autorenporträt

Kenneth A. Ross is currently an emeritus professor of mathematics at the University of Oregon. Jorge M. López is currently professor of mathematics at the University of Puerto Rico.

Inhaltsangabe

Preface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.

Rezensionen

From the reviews of the first edition:

"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer's opinion, has succeeded admirably." -- MATHEMATICAL REVIEWS

"This book occupies a niche between a calculus course and a full-blown real analysis course. ... I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis ... . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." -- Allen Stenger (The Mathematical Association of America, June, 2008)