The Origins of Cauchy's Rigorous CalculusCourier Corporation, 11 במאי 2012 - 272 עמודים This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition. |
מהדורות אחרות - הצג הכל
The Origins of Cauchy's Rigorous Calculus <span dir=ltr>Judith V. Grabiner</span> תצוגה מקדימה מוגבלת - 2011 |
מונחים וביטויים נפוצים
algebra of inequalities Ampère Ampère's analysis antiderivative applications approximation Arbogast Berkeley Berkeley's binomial series bounds Calcul des fonctions Calcul infinitésimal Cauchy calculus Cauchy and Bolzano Cauchy criterion Cauchy's Cauchy's definition Cauchy's proof Cauchy's theory century chapter compute continuous functions Cours d'analyse Cauchy curves d'Alembert d'analyse Cauchy 14 defined definite integral derivative difference differential equations discussion divergent series eighteenth Encyclopédie Equations numériques error Euler Euler's criterion example existence explicitly finite fluxions Fonctions analytiques Lagrange foundations geometry given Grattan-Guinness important infinite series infinitésimal Cauchy 14 instance intermediate-value theorem interval Iushkevich L'Huilier Lacroix Lagrange 16 Lagrange 9 Lagrange property Lagrange remainder Lagrange's Leçons Leibniz lemma limit concept Maclaurin mathe mathematicians mathematics mean-value theorem method Newton Newton's method notation paper Poisson polynomials power series problems prove quantities ratio real numbers Rein analytischer Beweis Struik tangent Taylor series Taylor's theorem techniques tion variable Weierstrass zero