Pierre-Simon, Marquis de Laplace (ləˈplɑ:s; pjɛʁ simɔ̃ laplas; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.
Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to suggest an idea similar to that of a black hole.
Laplace is regarded as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of almost all of his contemporaries.
He was Napoleon's examiner when Napoleon graduated from the École Militaire in Paris in 1785. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.
Some details of Laplace's life are not known, as records of it were burned in 1925 with the family château in Saint Julien de Mailloc, near Lisieux, the home of his great-great-grandson the Comte de Colbert-Laplace. Others had been destroyed earlier, when his house at Arcueil near Paris was looted in 1871.
Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749, a village four miles west of Pont l'Évêque. According to W. W. Rouse Ball, his father, Pierre de Laplace, owned and farmed the small estates of Maarquis.
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In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller.
In linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.
Baron Siméon Denis Poisson FRS FRSE (si.me.ɔ̃ də.ni pwa.sɔ̃; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid mechanics. Moreover, he predicted the Poisson spot in his attempt to disprove the wave theory of Augustin-Jean Fresnel, which was later confirmed.
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2023
. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...