He lived 1642 to 1708, invented calculus, and used determinants [1683]. Japanese temple geometry flourished at this time.
He lived 1652 to 1719 and invented Rolle's theorem [1691].
He lived 1700 to 1782. He solved differential equations by isolating variables. He developed cylindrical and spherical wave equations to represent organ-pipe sounds. He invented vibrating string equation. He studied hydrodynamics and invented Bernoulli's law [1734].
He lived 1698 to 1759 and developed dynamics maximizing-minimizing principle (principle of least action or least-action principle or principle of stationary action or stationary-action principle).
He lived 1736 to 1813 and studied calculus of variations, mean-value theorem, spherical coordinates, solution envelopes, adjoint equations, finite-differences method, and perturbation methods. He solved differential-equation systems using conic-section deviations. Newton's laws can depend on principle of stationary action in Euler-Lagrange equations. Natural numbers are sums of four natural-number squares.
He lived 1717 to 1783 and studied differential equations and multiple integrals and invented d'Alembert's test. He found that Newton's 3rd law applies to free bodies {d'Alembert's principle}.
He lived 1749 to 1827 and studied partial differential equations, Laplace transforms and operators, perturbations method, spherical coordinates, finite-differences method, and divergence theorem.
After proving that planetary elliptical orbits can be stable, he said, "Je n'avais pas besoin de cette hypothèse-là" or "I had no need of that hypothesis" when asked by Napoleon why he did not invoke God to explain solar-system stability, as Newton had thought necessary because of chaotic conditions (which are there but just small enough).
Epistemology
Given physical laws and particle motions and positions, people can predict everything in the future.
Metaphysics
Solar system formed from spinning gas cloud {nebular hypothesis}. Gravity and motion correct planetary-orbit perturbations, rather than causing chaos.
He lived 1793 to 1841, invented Green's theorem, and studied double integrals, line integrals, and curvilinear integrals.
He lived 1809 to 1882 and invented Sturm-Liouville theory [1829 and 1837] and transcendental numbers [1851]. Phase-space region volume is constant for Hamiltonian equation {Liouville's theorem, Liouville}, but volumes spread into larger space, leaving empty spaces.
He lived 1795 to 1870 and studied curvilinear coordinates [1840] and invented Lamé's differential equation.
He lived 1819 to 1903 and invented Stokes theorem [1845], fluid-dynamics Navier-Stokes equations, and Stokes lines. Navier-Stokes equations extend Newton's second dynamics law and linear constitutive stress relation.
He lived 1831 to 1889 and classified partial differential equations.
He lived 1856 to 1894 and invented Stieltjes integral.
He lived 1888 to 1970 and solved differential equations by substituting algebraic equations {relaxation method, Southwell}.
He lived 1918 to 1974 and developed the idea of infinitesimals as greater than zero but smaller than all positive numbers {nonstandard analysis, Robinson}. He described infinitesimal neighborhoods of points infinitely close to a point {compactness theorem, Robinson}.
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Date Modified: 2022.0225