Description
(Table of content)
1 Propaedeutic.- 2 Institutions and individuals around the 1800s.- 3 The 18th-century heritage: the calculus around 1800.- 4 The Lagrangian tradition in the calculus, 1800-1815.- 5 The 18th-century heritage: mechanics around 1800.- 6 Progress in mechanics, 1800-1815.- 7 Laplace's mathematicised molecular physics, 1804-1816.- 8 Aspects of engineering mathematics, 1800-1816.- 9 The entry of Fourier: heat theory and Fourier analysis, 1800-1816.- 10 The entry of Cauchy: complex variables and differential equations, 1810-1822.- 11 Cauchy's inauguration of mathematical analysis, 1820-1827.- 12 The consolidation of heat theory, 1816-1825.- 13 The entry of Fresnel: physical optics, 1815-1824.- 14 The entry of physicist Ampère: electricity and magnetism, especially their connections, 1820-1826.- 15 The entry of Navier and the triumph of Cauchy: elasticity theory, 1819-1830.- 16 Work for the workers: engineering mechanics and its instruction, 1800-1830.- 17 Towards the 1830s: the new generation.- 18 Towards the 1840s: epilogue.- 19 Chorus.- 20 Texts of selected manuscripts and printings.- 21 Tables.- 22 Bibliography.- 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.ed 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 achie
Contents
1 Propaedeutic.- 2 Institutions and individuals around the 1800s.- 3 The 18th-century heritage: the calculus around 1800.- 4 The Lagrangian tradition in the calculus, 1800-1815.- 5 The 18th-century heritage: mechanics around 1800.- 6 Progress in mechanics, 1800-1815.- 7 Laplace's mathematicised molecular physics, 1804-1816.- 8 Aspects of engineering mathematics, 1800-1816.- 9 The entry of Fourier: heat theory and Fourier analysis, 1800-1816.- 10 The entry of Cauchy: complex variables and differential equations, 1810-1822.- 11 Cauchy's inauguration of mathematical analysis, 1820-1827.- 12 The consolidation of heat theory, 1816-1825.- 13 The entry of Fresnel: physical optics, 1815-1824.- 14 The entry of physicist Ampère: electricity and magnetism, especially their connections, 1820-1826.- 15 The entry of Navier and the triumph of Cauchy: elasticity theory, 1819-1830.- 16 Work for the workers: engineering mechanics and its instruction, 1800-1830.- 17 Towards the 1830s: the new generation.- 18 Towards the 1840s: epilogue.- 19 Chorus.- 20 Texts of selected manuscripts and printings.- 21 Tables.- 22 Bibliography.- 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.
