LaCroix and the Calculus

ISBN-13: 9783764386375 / Angielski / Twarda / 2008 / 468 str.

Joao Caramalho Domingues

Opis

Silvestre Francois Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traite du calcul differentiel et du calcul integral (1797-1800; 2^nd ed. 1810-1819) an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19^th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix s large Traite. It uses the unique and massive bibliography given by Lacroix to explore late 18^th-century calculus, and the way it is reflected in Lacroix s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). "

Recenzje

From the reviews:
"The present book is a thorough presentation of the calculus from Lacroix's point of view ... . Lacroix and the calculus concludes with four appendices, a Bibliography (thirty-three pages), and an index. ... Anyone interested in the history of the calculus will find this book to be of great interest and value in his or her own studies." (F. J. Papp, Mathematical Reviews, Issue 2011 i)

Spis treści

Introduction.- A short biography of Silvestre-François Lacroix.- An overview of Lacroix’s Traité.- The principles of the calculus.- Analytic and differential geometry.- Approximate integration and conceptions of the integral.- Types of solutions of differential equations.- Aspects of differences and series.- The Traité élémentaire.- The second edition of the Traité.- final remarks.- Two memoirs by Lacroix.- Lacroix’s historical appraisal of his own Traité.- Syllabi of Lacroix’s course of analysis at the École Polytechnique.- Biographical data on a few obscure characters.- Bibliography.

Blurb

Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2^nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19^th century, in spite of Cauchy's reform of the subject in the 1820's.

Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18^th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions).

Lacroix’s large Traité... was adapted for teaching into a shorter, textbook version – the Traité élémentaire de calcul différentiel et de calcul intégral (1802; several later editions). This adaptation is also analysed.

Lacroix and the Calculus should appeal to historians and mathematicians interested in the history of the calculus (and especially in the background to Cauchy and Bolzano) and in its teaching in the late 18^th and early 19^th centuries.