History and Hermeneutics for Mathematics Education
Storia
ed Ermeneutica per la Didattica della Matematica
Calculus by De Morgan (1842)
Il Calculus di De Morgan (1842)
De Morgan, A. (1842), The differential and integral Calculus,
Baldwin and Cradock,
DE MORGAN Augustus (1806-1871)
Contents.
Introductory chapter.
Chapter I. On
the processes of direct differentiation.
Chapter II. On
the general theory of functional increments and differentiation.
Chapter III. On
algebraical development.
Chapter IV. Calculus
of finite differences.
Chapter V. On
implicit differentiation.
Chapter VI. Meaning
of, and processes in, integration.
Chapter VII. Trigonometrical
analysis.
Chapter VIII. On
the meaning of differential coefficients, and of the first principles of the
application of the science to geometry and mechanics.
Chapter IX. On
the connexion of differentiations of different kinds.
Chapter X. On
singular values.
Chapter XI. On
differential equations.
Chapter XII. Further
application to algebra.
Chapter XIII. Miscellaneous
examples and developments.
Chapter XIV. Application
to geometry of two dimensions.
Chapter XV. Application
to geometry of three dimensions.
Chapter XVI. On
the calculus of variations.
Chapter XVII. Application
to mechanics.
Chapter XVIII. On
interpolation and summation.
Chapter XIX. On
the transformation of divergent developments.
Chapter XX. On definite integrals.
Chapter XXI. On
differential equations and equations of differences.
Appendix.
See moreover:
Si veda inoltre:
L’Hospital, G. de (1716), Analyse
des infiniment petits, Papillon, Paris (II ed.).
Newton, I. (1740), Le methode des fluxions et
des suites infinites, Debure, Paris (I ed.: 1736).
Riccati,
V. (1752), De
usu motus tractorii in constructione Aequationum Differentialium Commentarius,
Lelio della Volpe, Bologna.
Paulini
a S. Josepho (P. Chelucci) (1755), Institutiones analyticæ earumque usus in
Geometria, Gessari, Napoli.
Torelli,
G. (1758), De
nihilo geometrico libri II, Carattoni, Verona.
Euler,
L. (1787) Institutiones
Calculi Differentialis cum eius usu in Analysi Finitorum ac Doctrina Serierum,
I, II, Galeati, Pavia (II ed.; I ed.: 1755).
Euler,
L. (1796), Introduction
a l’Analyse Infinitésimale, I, II, Barrois, Paris (I ed. in French).
Brunacci,
V. (1804), Corso
di Matematica sublime, I, II, Allegrini, Firenze.
Lagrange, J.L. (1813), Théorie
des fonctions analytiques, Courcier, Paris.
Cauchy, A.L. (1836), Vorlesungen uber die Differenzialrechung,
Meyer, Braunschweig.
Lacroix, S.F. (1837), Traité
elementaire du Calcul Différentiel et du Calcul Intégral, Bachelier, Paris
(V ed.).
Carmichael, R. (1855), A
Treatise on the Calculus of Operations, Longman, Brown, Green and Longmans,
Sturm, Ch. (1868), Cours d’Analyse, I, II,
Gauthier-Villars, Paris.
Carnot, L.N.M. (1881), Réflections
sur la métaphisique du Calcul Infinitésimal, Gauthier-Villars, Paris (I
ed.: 1797).
Laurent, H. (1885-1887-1888), Traité
d’Analyse, I, II, III, Gauthier-Villars, Paris.
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History and Hermeneutics for Mathematics Education
(Giorgio T. Bagni, Editor)
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