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Unformatted text preview: ◦ Volterra constructed a function that was differentiable everywhere but whose derivative was not Riemann-integrable. Textbooks • L’Hôpital (1696) ◦ Analyse des infiniment petits pour l’intelligence des lignes courbes (Analysis of the In- finitely Small for the Understanding of Curved Lines) ◦ The first Calculus textbook. ◦ The things he learned from Johann Bernoulli. ◦ “L’Hôpital’s Rule” is really Johann Bernoulli’s rule. • Euler (1755 and 1768) ◦ Institutiones calculi differentialis in 1755. ◦ Institutiones calculi integralis in 1768 (3 volumes). ◦ A total of over 2000 pages. ◦ Studied by many prominent mathematicians of the 19th century. • Cauchy ◦ Course d’analyse de l’École Royale Polytechnique in 1821. ◦ Résumeé des leçons données a l’École Royale Polytechnique, sur le calcul infinitésimal in 1823. ◦ Stated and proved the Intermediate Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus....
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
- Fall '10