Robert E. Bradley, C. Edward Sandifer

Cauchy's Cours d'analyse (eBook, PDF)

An Annotated Translation

• Format: PDF

Produktbeschreibung

This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the most influential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements.

The authors' style mimics the look and feel of the second French edition. It is an essentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially "Euclidean architecture" in its careful ordering of definitions and theorems. It was the first book in analysis to do this.

Cauchy's book is essentially a precalculus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of the volume.

The basicaudience is anyone interested in the history of mathematics, especially 19th century analysis.

In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill to read.

Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 412
• Erscheinungstermin: 14. Januar 2010
• Englisch
• ISBN-13: 9781441905499
• Artikelnr.: 37360807

Inhaltsangabe

On real functions..- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases..- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions..- Determination of integer functions, when a certain number of particular values are known. Applications..- Determination of continuous functions of a single variable that satisfy certain conditions..- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series..- On imaginary expressions and their moduli..- On imaginary functions and variables..- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series..- On real or imaginary roots of algebraic equationsfor which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry..- Decomposition of rational fractions..- On recurrent series..

Rezensionen

From the book reviews:

"The annotations show that the translators had not only the expert historian in mind, but also a general mathematical reader. Apparently, beginning students of mathematics are also intended as possible readers. ... This is not only useful for a reader with a better command of English than of French, but also for anybody who intends to write a professional historical paper in English in which he has to quote from Cauchy's book. This book is useful and well done." (Hans Niels Jahnke, Historia Mathematica, Vol. 39, 2012)

"The majority of mathematical activity now takes place in English ... so this translation is especially welcome. ... It is a mathematical delight to read through this book. ... Cauchy carefully built the subject up from the most elementary ideas in algebra and arithmetic. ... Readers of this review should encourage their libraries to get this book, and anyone interested in the history of mathematical analysis will want to own a copy." (Judith V. Grabiner, BSHM Bulletin, Vol. 26, 2011)

"Bradley (Adelphi Univ.) and Sandifer (Western Connecticut State Univ.) have written an annotated, indexed translation of Cauchy's classic textbook from 1821. The work's most interested readers will probably be students and researchers of the history and philosophy of mathematics education, and education in general. ... it will be valuable for specialized historical collections. Summing Up: Essential. ... academic history of mathematics education and history of science collections, lower-division undergraduates and above." (M. Bona, Choice, Vol. 47 (6), February, 2010)

"It covers real functions, continuity, simultaneous linear equations, interpolation by polynomials, special functional equations, convergent and divergent series, complex numbers, functions and series, the fundamental theorem of algebra, the numerical solution of equations and infinite products, among other things. The translators provide a preface, about 200 (mostly brief) footnotes and a bibliography of 64 items. ... The footnotes and bibliography give, or lead to, useful information on historical questions." (M. E. Muldoon, Mathematical Reviews, Issue 2010 h)

"The book under review comes equipped with a well-written Translator's Preface, full of interesting and relevant historical data, placing Cauchy's work in the present connection in the proper historical context. ... Cauchy's Cours d'analyse, An Annotated Translation is a major contribution to mathematical historical scholarship, and it is most welcome indeed to have occasion to examine the infancy of a part of modern analysis, to recognize familiar things in archaic and even arcane phrasings ... and, through it all, to witness a grandmaster in action." (Michael Berg, The Mathematical Association of America, November, 2009)

From the reviews: "The book under review comes equipped with a well-written Translator's Preface, full of interesting and relevant historical data, placing Cauchy's work in the present connection in the proper historical context. ... Cauchy's Cours d'analyse, An Annotated Translation is a major contribution to mathematical historical scholarship, and it is most welcome indeed to have occasion to examine the infancy of a part of modern analysis, to recognize familiar things in archaic and even arcane phrasings ... and, through it all, to witness a grandmaster in action." (Michael Berg, The Mathematical Association of America, November, 2009) "Bradley (Adelphi Univ.) and Sandifer (Western Connecticut State Univ.) have written an annotated, indexed translation of Cauchy's classic textbook from 1821. The work's most interested readers will probably be students and researchers of the history and philosophy of mathematics education, and education in general. ... it will be valuable for specialized historical collections. Summing Up: Essential. ... academic history of mathematics education and history of science collections, lower-division undergraduates and above." (M. Bona, Choice, Vol. 47 (6), February, 2010) "It covers real functions, continuity, simultaneous linear equations, interpolation by polynomials, special functional equations, convergent and divergent series, complex numbers, functions and series, the fundamental theorem of algebra, the numerical solution of equations and infinite products, among other things. The translators provide a preface, about 200 (mostly brief) footnotes and a bibliography of 64 items. ... The footnotes and bibliography give, or lead to, useful information on historical questions." (M. E. Muldoon, Mathematical Reviews, Issue 2010 h) "The majority of mathematical activity now takes place in English ... so this translation is especially welcome. ... It is a mathematical delight to read through this book. ... Cauchy carefully built the subject up from the most elementary ideas in algebra and arithmetic. ... Readers of this review should encourage their libraries to get this book, and anyone interested in the history of mathematical analysis will want to own a copy." (Judith V. Grabiner, BSHM Bulletin, Vol. 26, 2011)