Resources For The Study Of Real Analysis

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Robert L. Brabenec - Collection Mathematics/Analysis

232 pages, parution le 04/04/2005

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Résumé

This book is a collection of materials gathered by the author while teaching real analysis over a period of years. It is intended for use as a supplement to a traditional analysis textbook, or to provide material for seminars or independent study in analysis and its historical development. The book includes historical and biographical information, a wide range of problem types, selected readings on a variety of topics, and many references for additional study. Since all these materials are collected into a single book, teachers and students can easily choose items most suitable for their purpose. Teachers may use the book as a supplement to their courses, while students may read much of the book on their own. No other book has been written specifically as a supplement for a real analysis course.

Part I provides a review of calculus for students beginning an analysis course, and includes a collection of twenty-five problems both to review calculus and to preview the content of analysis. Part II contains thirty-four detailed problems covering a wide variety of topics, including both worked examples and exercises. These are intended both to supplement the typical problem collections in analysis textbooks and to enrich the course with accessible problems on topics such as Bernoulli numbers, the gamma function, Fourier series, Lebesgue measure, and summability. Part III contains ten essays, six of which provide an historical overview of the ideas and individuals involved in the development of analysis. The other four essays discuss themes such as obtaining the derivative formulas, a unified presentation of tests for series convergence techniques, suggestions for understanding and writing proofs in analysis, and an overview of basic results about sets and topology. Part IV includes five selections dealing with topics such as the relationship between John Bernoulli and I'Hospital, the content of correspondence between Leonhard Euler and James Stirling, and the development of rigor in calculus. The annotated bibliography provides extensive descriptive information about several additional references.

Sommaire

Preface
Review of Calculus
Analysis Problem
Essays
Selected Readings
Annotated Bibliography
Additional References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Robert L. Brabenec
Collection	Mathematics/Analysis
Parution	04/04/2005
Nb. de pages	232
Format	18 x 26
Couverture	Relié
Poids	601g
Intérieur	Noir et Blanc
EAN13	9780883857373
ISBN13	978-0-88385-737-3