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The differential: Nineteenth and twentieth century developments. (English) Zbl 0289.01015


MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
26-03 History of real functions
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[1] Carathéodory, C., Vorlesungen über Reelle Funktionen. Leipzig: Teubner, 1927. (This is the second edition; the first edition was published in 1918.) · JFM 46.0376.12
[2] Cauchy, A. L., Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal. Paris, 1823.
[3] Dieudonné, J., Foundations of Modern Analysis. New York: Academic Press 1960. · Zbl 0100.04201
[4] Paul du Bois-Reymond, Die Allgemeine Functionentheorie, I, Tübingen, 1882.
[5] Duhamel, J. M. C., Cours d’Analyse de l’École Polytechnique, première partie, Paris, 1841. (I have not seen earlier editions.)
[6] Duhamel, J. M. C., Élements de calcul infinitésimal (revue et annotée parM. J. Bertrand), third edition, Paris, 1874.
[7] Fréchet, M., Sur la notion de différentielle, Comptes rendus de l’Académie des Sciences, Paris,152, 845-847 (1911). · JFM 42.0305.05
[8] Fréchet, M., Sur la notion de différentielle,ibid., 1050-1051 · JFM 42.1030.04
[9] Fréchet, M., Sur la notion de différentielle totale, Nouvelles Annales de Mathématiques, Paris, ser. 4,12, 385-403 and 433-449 (1912). · JFM 43.0481.03
[10] Fréchet, M., Sur la notion de différentielle dans le Calcul Fonctionnel, Comptes rendus du Congrès des Societés savantes, Paris, 45-59 (1912).
[11] Fréchet, M., Sur la notion de différentielle totale,ibid., 5-8 (1915).
[12] Fréchet, M., La notion de différentielle dans l’analyse générale, Annales Scientifiques de l’École Normale Supérieure, ser. 3,42, 293-323 (1925). · JFM 51.0312.03
[13] Genocchi, A., &G. Peano, Calcolo differenziale e principii di calcolo integrale, Torino, 1884. · JFM 16.0223.01
[14] Genocchi, A., &G. Peano, German translation of the foregoing byG. Bohlmann & A. Schepp. Differentialrechnung und Grundzüge der Integralrechnung. Leipzig: Teubner 1899.
[15] Graves, L. M., Topics in the Functional Calculus, Bulletin of the American Mathematical Society,41, 641-662 (1935). · Zbl 0013.02502 · doi:10.1090/S0002-9904-1935-06162-2
[16] Hadamard, J., Leçons sur le Calcul des Variations, Tome premier. Paris: Hermann 1910. · JFM 41.0432.02
[17] Harnack, A., Die Elemente der Differential- und Integralrechnung, Leipzig, 1881. · JFM 13.0202.02
[18] Hildebrandt, T. H., &L. M. Graves, Implicit Functions and their Differentials in General Analysis, Transactions of the American Mathematical Society29, 127-153 (1927). · JFM 53.0234.02 · doi:10.1090/S0002-9947-1927-1501380-6
[19] Hille, E., Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, New York, 1948. · Zbl 0033.06501
[20] Hille, E., &R. S. Phillips, revised edition of [19], with same title, Providence, 1957.
[21] Hobson, E. W., Theory of Functions of a Real Variable and the Theory of Fourier Series, 3rd edition, Cambridge University Press, 1927. (Unaltered reprint by Dover, New York, 1957.) The first edition is dated 1907. · JFM 38.0414.01
[22] Otto Hölder, Beiträge zur Potentialtheorie, Stuttgart, 1882. (This isHölder’s doctoral dissertation at Tübingen.)
[23] Jordan, C., Cours d’Analyse de l’École Polytechnique, tome prémier ? Calcul différentiel, Paris, 1882. Second edition, 1893; third edition, 1909. · JFM 24.0247.03
[24] Lacroix, S. F., Traité du Calcul Différentiel et du Calcul Intégral, Tome I, Paris, 1810, second edition. I have not seen the first edition of 1797.
[25] Lagrange, J. L., Leçons sur le Calcul des Fonctions, Nouvelle Édition, Paris, 1806. The first edition, which I have not seen, was published in 1801.
[26] Lévy, P., Leçons d’Analyse Fonctionnelle. Paris: Gauthier-Villars, 1922. · JFM 48.0453.01
[27] Michal, A. D., Le Calcul Différentiel dans les Espaces de Banach. Paris: Gauthier-Villars, 1958. · Zbl 0083.10901
[28] Nevanlinna, F. &, Absolute Analysis. Berlin, Göttingen, Heidelberg: Springer 1959.
[29] Osgood, W. F., Advanced Calculus, New York: Macmillan 1925. · JFM 51.0172.07
[30] Ostrowski, A., Vorlesungen über Differential- und Integralrechnung, Band 2. Basel: Birkhäuser, 1951. · Zbl 0044.27501
[31] Moritz Pasch, Einleitung in die Differential- und Integralrechnung, Leipzig, 1882. · Zbl 0328.50001
[32] Peano, G., Lezioni di Analisi Infinitesimale, vols.1,2, Torino, 1893.
[33] Peano, G., seeGenocchi &Peano.
[34] Pierpont, J., Lectures on the Theory of Functions of Real Variables. Boston: Ginn, 1905. · JFM 36.0346.01
[35] Pringsheim, A., Grundlagen der Allgemeinen Funktionenlehre, Part II A 1, pp. 1-53, from Encyclopädie der Mathematischen Wissenschaften, II:1:1, Leipzig, 1899-1916.
[36] Raabe, J. L., Die Differenzial- und Integralrechnung, Band1, mit Functionen einer Variabeln, Zürich, 1839.
[37] Raabe, J. L., Die Differenzial- und Integralrechnung, Band2, mit Functionen mehrerer Variabeln, Zurich, 1843.
[38] Serret, J. A., Lehrbuch der Differential- und Integralrechnung, Band I, second German edition, edited byG. Bohlmann. Leipzig, 1897. Translated from the French byA. Harnack. I have not seen the first German edition of 1884.
[39] Sherwood, G. E. F., &A. E. Taylor, Calculus. New York: Prentice-Hall, 1942.
[40] Stolz, O., Grundzüge der Differential- und Integralrechnung, Erster Theil: Reelle Veränderliche und Functionen, Leipzig: Teubner 1893. · JFM 25.0447.01
[41] Sturm, C., Cours d’Analyse de l’École Polytechnique, tome 1, Paris, 1880. · JFM 16.0226.03
[42] Taylor, A. E., Advanced Calculus, Boston: Ginn, 1955. · Zbl 0067.02503
[43] Taylor, A. E., Historical Notes on Analyticity as a Concept in Functional Analysis, pp. 325-343 in Problems in Analysis?A Symposium in Honor of Salomon Bochner, Princeton University Press, 1970.
[44] Thomae, J., Abriss einer Theorie der complexen Functionen und der Thetafunctionen einer Veränderlichen, Zweite vermehrte Auflage, Halle, 1873. (The first edition, which I have not seen, was published in 1870.)
[45] Thomae, J., Einleitung in die Theorie der bestimmten Integrale, Halle, 1875.
[46] de la Vallée Poussin, Ch. J., Cours d’Analyse Infinitésimale, Tome 1, troisième édition, Louvain and Paris, 1914. · JFM 45.0432.14
[47] Voss, A., Differential- und Integralrechnung, Part II A 2, pp. 54-134 from Encyclopädie der Mathematischen Wissenschaften, II: 1:1, Leipzig, 1899-1916.
[48] Young, W. H., Un théorème sur les différentielles. Comptes rendus de l’Académie des Sciences, Paris,148, 82-84 (1909).
[49] Young, W. H., On Differentials, Proceedings of the London Mathematical Society, ser. 2,7, 157-180 (1909). · JFM 40.0333.02 · doi:10.1112/plms/s2-7.1.157
[50] Young, W. H., On Implicit Functions and Their Differentials,ibid., 397-421. · JFM 40.0333.03
[51] Young, W. H., The Fundamental Theorems of the Differential Calculus, Cambridge Tracts in Mathematics, No. 11, Cambridge University Press, 1910. · JFM 41.0306.01
[52] Zorn, M. A., Derivatives and Fréchet Differentials, Bulletin of the American Mathematical Society,52, 133-137 (1946). · Zbl 0061.25002 · doi:10.1090/S0002-9904-1946-08524-9
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