Beschreibung
Neuware -Inhaltsangabe1 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 'Ela.
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