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.
