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Produktbild: Convolutions in French Mathematics, 1800–1840

Convolutions in French Mathematics, 1800–1840 From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics

Aus der Reihe Science Networks. Historical Studies

Fr. 191.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Set mit diversen Artikeln

Erscheinungsdatum

19.01.2013

Verlag

Springer Basel

Seitenzahl

1602

Maße (L/B/H)

24.4/17/8.7 cm

Gewicht

2755 g

Auflage

Softcover reprint of the original 1st ed. 1990

Sprache

Englisch

ISBN

978-3-0348-9918-5

Beschreibung

Produktdetails

Einband

Set mit diversen Artikeln

Erscheinungsdatum

19.01.2013

Verlag

Springer Basel

Seitenzahl

1602

Maße (L/B/H)

24.4/17/8.7 cm

Gewicht

2755 g

Auflage

Softcover reprint of the original 1st ed. 1990

Sprache

Englisch

ISBN

978-3-0348-9918-5

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Convolutions in French Mathematics, 1800–1840
  • 1 Propaedeutic.- 1.1 Gobbets.- 1.2 Micropaedia.- 1.3 On the philosophy of mathematics.- 1.4 On the historiography of mathematics.- 1.5 On the organisation of the text.- 2 Institutions and individuals around the 1800s.- 2.1 Plan of the chapter.- 2.2 Research at the Institut and elsewhere.- 2.3 Education at the Ecole Polytechnique.- 2.4 Other schools, mostly in Paris.- 2.5 Major and minor figures.- 2.6 New men and a new profession.- 3 The 18th-century heritage: the calculus around 1800.- 3.1 Plan of the chapter.- 3.2 The foundations of the calculus in the late 18th century.- 3.3 On differential equations.- 3.4 On series, functions and integrals.- 3.5 On differences, interpolation and tables.- 3.6 Concluding comments: the aspirations of Lacroix 183.- 4 The Lagrangian tradition in the calculus, 1800–1815.- 4.1 Plan of the chapter.- 4.2 New figures, and a new journal.- 4.3 Consequences of Lagrange: functions and the new algebras.- 4.4 Differential and difference equations.- 4.5 On the calculus of variations.- 4.6 Equations and their roots.- 4.7 Case studies in the relationship between geometry and algebra.- 4.8 Concluding comments.- Interlude 480.1 The calculus outside France.- 5 The 18th-century heritage: mechanics around 1800.- 5.1 Prefaces.- 5.2 Principles and scope of mechanics in the late 18th century.- 5.3 Two main results, and their various proofs.- 5.4 On celestial mechanics.- 5.5 On planetary mechanics.- 5.6 Concluding comment: the aspirations of Laplace.- Interlude 525.1 Notes on handling differential models in mathematical physics.- 6 Progress in mechanics, 1800–1815.- 6.1 Prefaces.- 6.2 Research and education in terrestrial mechanics.- 6.3 Variational mechanics: the Poisson and Lagrange brackets, 1808–1810.- 6.4 Celestial and planetary mechanics—with statistics.- 6.5 Potential theory and the pendulum.- 6.6 Concluding comments.- Interlude 641.1 Notes on German theoretical astronomy.- Interlude 660.1 Mechanics outside France.- 7 Laplace’s mathematicised molecular physics, 1804–1816.- 7.1 Prefaces.- 7.2 The first steps.- 7.3 Poisson versus Germain on elastic surfaces, 1811–1815.- 7.4 On Laplacian optics.- 7.5 On Newtonian electricity and magnetism.- 7.6 Poisson’s inauguration of mathematical electrostatics, 1812–1813.- 7.7 Concluding comment: the aspirations of the Laplacians.- 8 Aspects of engineering mathematics, 1800–1816.- 8.1 Prefaces.- 8.2 Some principal figures and organisations.- 8.3 Perspectives on descriptive geometry.- 8.4 On the engineering science of materials.- 8.5 On the engineering studies of fluids.- 8.6 Concluding comment: the spectrum of engineering mathematics.- Interlude 860.1 On engineering outside France.- 9 The entry of Fourier: heat theory and Fourier analysis, 1800–1816.- 9.1 Prefaces.- 9.2 The diffusion equation and its series solutions.- 9.3 Reactions and further results, 1808–1815.- 9.4 Fourier’s prospects.- 9.5 Concluding comment: the aspirations of Fourier.- Interlude 934.1 Notes on the history of the Laplace transform.- 10 The entry of Cauchy: complex variables and differential equations, 1810–1822.- 10.1 Prefaces.- 10.2 Complex variables and the evaluation of integrals, 1810–1815.- 10.3 Poisson and Cauchy on the propagation of waves, 1815-1817.- 10.4 Competing solutions to linear partial differential equations, 1818-1822.- 10.5 Concluding comment: the aspirations of Cauchy.- 11 Cauchy’s inauguration of mathematical analysis, 1820–1827.- 11.1 Prefaces.- 11.2 On the general theory of partial differential equations to 1820.- 11.3 Cauchy on the primacy of limits: the Cours d’analyse, 1821.- 11.4 Integrals, real and complex, 1820–1823.- 11.5 Cauchy’s calculus, real and complex, 1823–1827.- 11.6 Miscellaneous studies of the mid 1820s.- 11.7 Concluding comments: the position of Cauchy.- Interlude 1170.1 Notes on mathematical analysis outside France.- 12 The consolidation of heat theory, 1816–1825.- 12.1 Plan of the chapter.- 12.2 New studies of the physics of heat.- 12.3 ‘Elastic fluids’ and the velocity of sound with Laplace and Poisson, 1816–1823.- 12.4 Planetary heat theory with Fourier and Laplace, 1817–1820.- 12.5 Heat diffusion and radiation with Poisson and Fourier, 1821 to 1825.- 12.6 Concluding comment: heat theory in textbooks and treatises.- 13 The entry of Fresnel: physical optics, 1815–1824.- 13.1 Prefaces.- 13.2 The battle over diffraction, 1815–1819.- 13.3 Fresnel’s developing theories, 1816–1821.- 13.4 The victory over double refraction, 1819–1822.- 13.5 The consolidation of Fresnel’s theory, 1822–1823.- 13.6 Concluding comments.- Interlude 1361.1 On Fresnel’s work on lighthouse lamps.- 14 The entry of physicist Ampère: electricity and magnetism, especially their connections, 1820–1826.- 14.1 Prefaces.- 14.2 Ampère’s first moves, 1820–1822.- 14.3 Ampère’s supporters, 1823.- 14.4 The consolidation of Ampère’s theory, 1824–1826.- 14.5 Poisson’s further studies of magnetism, 1825–1826.- 14.6 Concluding comments 965 14.6.1 The isolated achievements of Ampère and Poisson.- 14.6.2 Laplace on problems in physics, 1825.- 15 The entry of Navier and the triumph of Cauchy: elasticity theory, 1819–1830.- 15.1 Plan of the chapter.- 15.2 The entry of Navier.- 15.3 Navier’s applied elasticity theory, 1823–1826.- 15.4 Cauchy’s inauguration of linear elasticity theory, 1827–1829.- 15.5 Poisson’s molecular elasticity theory, 1827–1829.- 15.6 Extensions of elasticity theories, 1828–1830.- 15.7 Concluding comment: the theories of elasticity.- 16 Work for the workers: engineering mechanics and its instruction, 1800–1830.- 16.1 Prefaces.- 16.2 New figures and their institutions.- 16.3 Concepts of work from Euler to Navier.- 16.4 Coriolis and Poncelet on ‘work’ in mechanics, 1829.- 16.5 Contemporary case studies in the concept of work.- 16.6 Educating the workers in work.- 16.7 Concluding comments: the aspirations for work.- 17 Towards the 1830s: the new generation.- 17.1 Prefaces.- 17.2 Aspects of mathematical analysis.- 17.3 Aspects of algebra.- 17.4 Aspects of corporeal mechanics.- 17.5 Mostly heat theory.- 17.6 Aspects of celestial and planetary mechanics.- 17.7 Aspects of engineering and its economy.- 17.8 Concluding comments: a change of air.- Interlude 1754.1 Paris mathematics in Ohm and Green.- 18 Towards the 1840s: epilogue.- 18.1 Plan and purpose of the chapter.- 18.2 Into the 1830s.- 18.3 Coda: into the 1840s.- 19 Chorus.- 19.1 Plan of the chapter.- 19.2 The savants and their institutions.- 19.3 The savants and their community.- 19.4 The savants and their achievements.- 19.5 A self-appraisal: the desimpliflcation of history.- 19.6 Gobbets.- 20 Texts of selected manuscripts and printings.- 20.1 Letter from Biot to Lacroix, 1800 (?).- 20.2 Report to the Ecole Polytechnique by Lacroix, 1805.- 20.3 Draft letter from Lacroix to F. J. Français.- 20.4 Extracts of a letter from Duchayla to Poinsot, 1813.- 20.5 Changed passages in Fourier’s book on heat diffusion, 1822.- 20.6 Letter from Ampère to P. Erman, 1823.- 20.7 Selections from notes by Poncelet on mechanics, 1825.- 20.8 Selections from de Prony’s criticisms of Cauchy at the Ecole Polytechnique, 1826–1829.- 20.9 Changed passages in the preface of Coriolis’s book on mechanics, 1829.- 20.10 Selections from minutes of the Paris Faculté on Hachette’s successor, 1834.- 20.11 Selections from a report by Coriolis to the Ecole Polytechnique, 1840.- 21 Tables.- 21.1 Career details of the major figures.- 21.2 Personnel and students at the Ecole Polytechnique.- 21.3 Chronological summary.- 22 Bibliography.- 22.1 Order.- 22.2 References.- 22.3 Journals.- 22.4 Abbreviations.- 22.5 Items.- 23 Indexes.- 23.1 Explanatory introduction.- 23.2 Index of persons and their work.- 23.3 Index of institutions and publications.- 23.4 Index of subjects.