Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Stahl, Saul
Titre(s) : Real analysis [Texte électronique] : a historical approach / Saul Stahl
Édition : 2nd ed.
Publication : Hoboken, NJ : Wiley, cop. 2011
Description matérielle : 1 online resource (1 texte électronique (xv, 297 p.))
Collection : Pure and applied mathematics
Note(s) : In Wiley online library. - Titre de l'écran-titre (visionné le 7 décembre 2011)
A provocative look at the tools and history of real analysis. This new edition of
"Real Analysis: A Historical Approach " continues to serve as an interesting read
for students of analysis. Combining historical coverage with a superb introductory
treatment, this book helps readers easily make the transition from concrete to abstract
ideas. The book begins with an exciting sampling of classic and famous problems first
posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton,
and Euler are each summoned in turn, illuminating the utility of infinite, power,
and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops
the basic tools of advanced calculus, which introduce the various aspects of the completeness
of the real number system as well as sequential continuity and differentiability and
lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter
on the Riemann integral, including the subject of uniform continuity, Explicit coverage
of the epsilon-delta convergence, A discussion of the modern preference for the viewpoint
of sequences over that of series, Throughout the book, numerous applications and examples
reinforce concepts and demonstrate the validity of historical methods and results,
while appended excerpts from original historical works shed light on the concerns
of influential mathematicians in addition to the difficulties encountered in their
work. Each chapter concludes with exercises ranging in level of complexity, and partial
solutions are provided at the end of the book
Sujet(s) : Analyse mathématique
Indice(s) Dewey : 515.8 (23e éd.) = Fonctions de variables réelles
Identifiants, prix et caractéristiques : ISBN 9781118096864
Identifiant de la notice : ark:/12148/cb446525797
Notice n° :
FRBNF44652579
(notice reprise d'un réservoir extérieur)
Table des matières : Archimedes and the Parabola ; Fermat, Differentiation, and Integration ; Newton's Calculus (Part 1) ; Newton's Calculus (Part 2) ; Euler ; The Real Numbers ; Sequences and Their Limits ; The Cauchy Property ; The Convergence of Infinite Series ; Series of Functions ; Continuity ; Differentiability ; Uniform Convergence ; The Vindication ; The Riemann Integral ; Appendix A: Excerpts from 'Quadrature of the Parabola' by Archimedes ; Appendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de Fermat ; Appendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton ; Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton ; Appendix E: Excerpts from 'Of Analysis by Equations of an Infinite Number of Terms' by Isaac Newton ; Appendix F: Excerpts from 'Subsiduum Calculi Sinuum' by Leonhard Euler ; Solutions to Selected Exercises.
