Search Results for Laplace


  1. Pierre-Simon Laplace (1749-1827)
    • Pierre-Simon Laplace .
    • Pierre-Simon Laplace's father, Pierre Laplace, was comfortably well off in the cider trade.
    • Laplace's mother, Marie-Anne Sochon, came from a fairly prosperous farming family who owned land at Tourgeville.
    • Many accounts of Laplace say his family were 'poor farming people' or 'peasant farmers' but these seem to be rather inaccurate although there is little evidence of academic achievement except for an uncle who is thought to have been a secondary school teacher of mathematics.
    • Laplace attended a Benedictine priory school in Beaumont-en-Auge, as a day pupil, between the ages of 7 and 16.
    • At the age of 16 Laplace entered Caen University.
    • However, during his two years at the University of Caen, Laplace discovered his mathematical talents and his love of the subject.
    • Credit for this must go largely to two teachers of mathematics at Caen, C Gadbled and P Le Canu of whom little is known except that they realised Laplace's great mathematical potential.
    • Once he knew that mathematics was to be his subject, Laplace left Caen without taking his degree, and went to Paris.
    • Although Laplace was only 19 years old when he arrived in Paris he quickly impressed d'Alembert.
    • Not only did d'Alembert begin to direct Laplace's mathematical studies, he also tried to find him a position to earn enough money to support himself in Paris.
    • Finding a position for such a talented young man did not prove hard, and Laplace was soon appointed as professor of mathematics at the Ecole Militaire.
    • Imparting geometry, trigonometry, elementary analysis, and statics to adolescent cadets of good family, average attainment, and no commitment to the subjects afforded little stimulus, but the post did permit Laplace to stay in Paris.
    • Laplace's first paper which was to appear in print was one on the integral calculus which he translated into Latin and published at Leipzig in the Nova acta eruditorum in 1771.
    • Six years later Laplace republished an improved version, apologising for the 1771 paper and blaming errors contained in it on the printer.
    • Laplace also translated the paper on maxima and minima into Latin and published it in the Nova acta eruditorum in 1774.
    • Also in 1771 Laplace sent another paper Recherches sur le calcul integral aux differences infiniment petites, et aux differences finies Ⓣ to the Melanges de Turin.
    • This paper contained equations which Laplace stated were important in mechanics and physical astronomy.
    • The year 1771 marks Laplace's first attempt to gain election to the Academie des Sciences but Vandermonde was preferred.
    • Laplace tried to gain admission again in 1772 but this time Cousin was elected.
    • Despite being only 23 (and Cousin 33) Laplace felt very angry at being passed over in favour of a mathematician who was so clearly markedly inferior to him.
    • D'Alembert also must have been disappointed for, on 1 January 1773, he wrote to Lagrange, the Director of Mathematics at the Berlin Academy of Science, asking him whether it might be possible to have Laplace elected to the Berlin Academy and for a position to be found for Laplace in Berlin.
    • Before Lagrange could act on d'Alembert's request, another chance for Laplace to gain admission to the Paris Academie arose.
    • We have already mentioned some of Laplace's early work.
    • Laplace's reputation steadily increased during the 1770s.
    • The 1780s were the period in which Laplace produced the depth of results which have made him one of the most important and influential scientists that the world has seen.
    • Although d'Alembert had been proud to have considered Laplace as his protege, he certainly began to feel that Laplace was rapidly making much of his own life's work obsolete and this did nothing to improve relations.
    • Laplace tried to ease the pain for d'Alembert by stressing the importance of d'Alembert's work since he undoubtedly felt well disposed towards d'Alembert for the help and support he had given.
    • It does appear that Laplace was not modest about his abilities and achievements, and he probably failed to recognise the effect of his attitude on his colleagues.
    • Lexell visited the Academie des Sciences in Paris in 1780-81 and reported that Laplace let it be known widely that he considered himself the best mathematician in France.
    • The effect on his colleagues would have been only mildly eased by the fact that Laplace was right! Laplace had a wide knowledge of all sciences and dominated all discussions in the Academie.
    • It was while Lexell was in Paris that Laplace made an excursion into a new area of science [',' Biography in Encyclopaedia Britannica.','2]:- .
    • Applying quantitative methods to a comparison of living and nonliving systems, Laplace and the chemist Antoine Lavoisier in 1780, with the aid of an ice calorimeter that they had invented, showed respiration to be a form of combustion.
    • Although Laplace soon returned to his study of mathematical astronomy, this work with Lavoisier marked the beginning of a third important area of research for Laplace, namely his work in physics particularly on the theory of heat which he worked on towards the end of his career.
    • In 1784 Laplace was appointed as examiner at the Royal Artillery Corps, and in this role in 1785, he examined and passed the 16 year old Napoleon Bonaparte.
    • In fact this position gave Laplace much work in writing reports on the cadets that he examined but the rewards were that he became well known to the ministers of the government and others in positions of power in France.
    • Laplace served on many of the committees of the Academie des Sciences, for example Lagrange wrote to him in 1782 saying that work on his Traite de mecanique analytique was almost complete and a committee of the Academie des Sciences comprising of Laplace, Cousin, Legendre and Condorcet was set up to decide on publication.
    • Laplace served on a committee set up to investigate the largest hospital in Paris and he used his expertise in probability to compare mortality rates at the hospital with those of other hospitals in France and elsewhere.
    • Laplace was promoted to a senior position in the Academie des Sciences in 1785.
    • Two years later Lagrange left Berlin to join Laplace as a member of the Academie des Sciences in Paris.
    • Laplace married on 15 May 1788.
    • His wife, Marie-Charlotte de Courty de Romanges, was 20 years younger than the 39 year old Laplace.
    • Laplace was made a member of the committee of the Academie des Sciences to standardise weights and measures in May 1790.
    • The weights and measures commission was the only one allowed to continue but soon Laplace, together with Lavoisier, Borda, Coulomb, Brisson and Delambre were thrown off the commission since all those on the committee had to be worthy:- .
    • Before the 1793 Reign of Terror Laplace together with his wife and two children left Paris and lived 50 km southeast of Paris.
    • Although Laplace managed to avoid the fate of some of his colleagues during the Revolution, such as Lavoisier who was guillotined in May 1794 while Laplace was out of Paris, he did have some difficult times.
    • Laplace knew well that the proposed scheme did not really work because the length of the proposed year did not fit with the astronomical data.
    • In 1795 the Ecole Normale was founded with the aim of training school teachers and Laplace taught courses there including one on probability which he gave in 1795.
    • Later Laplace wrote up the lectures of his course at the Ecole Normale as Essai philosophique sur les probabilites published in 1814.
    • Also in 1795 the Bureau des Longitudes was founded with Lagrange and Laplace as the mathematicians among its founding members and Laplace went on to lead the Bureau and the Paris Observatory.
    • Delambre also wrote concerning Laplace's leadership of the Bureau des Longitudes:- .
    • One can reproach [Laplace] with the fact that in more than 20 years of existence the Bureau des Longitudes has not determined the position of a single star, or undertaken the preparation of the smallest catalogue.
    • Laplace presented his famous nebular hypothesis in 1796 in Exposition du systeme du monde Ⓣ, which viewed the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
    • Laplace states his philosophy of science in the Exposition as follows:- .
    • In view of modern theories of impacts of comets on the Earth it is particularly interesting to see Laplace's remarkably modern view of this:- .
    • Exposition du systeme du monde Ⓣ was written as a non-mathematical introduction to Laplace's most important work Traite de Mecanique Celeste Ⓣ whose first volume appeared three years later.
    • Laplace had already discovered the invariability of planetary mean motions.
    • In it Laplace included a study of the shape of the Earth which included a discussion of data obtained from several different expeditions, and Laplace applied his theory of errors to the results.
    • Another topic studied here by Laplace was the theory of the tides but Airy, giving his own results nearly 50 years later, wrote:- .
    • It would be useless to offer this theory in the same shape in which Laplace has given it; for that part of the Mecanique Celeste which contains the theory of tides is perhaps on the whole more obscure than any other part..
    • In the Mecanique Celeste Ⓣ Laplace's equation appears but although we now name this equation after Laplace, it was in fact known before the time of Laplace.
    • The Legendre functions also appear here and were known for many years as the Laplace coefficients.
    • The Mecanique Celeste Ⓣ does not attribute many of the ideas to the work of others but Laplace was heavily influenced by Lagrange and by Legendre and used methods which they had developed with few references to the originators of the ideas.
    • Under Napoleon Laplace was a member, then chancellor, of the Senate, and received the Legion of Honour in 1805.
    • However Napoleon, in his memoirs written on St Helene, says he removed Laplace from the office of Minister of the Interior, which he held in 1799, after only six weeks:- .
    • Laplace became Count of the Empire in 1806 and he was named a marquis in 1817 after the restoration of the Bourbons.
    • The first edition of Laplace's Theorie Analytique des Probabilites Ⓣ was published in 1812.
    • The second book contains Laplace's definition of probability, Bayes rule (so named by Poincare many years later), and remarks on moral and mathematical expectation.
    • Applications to mortality, life expectancy and the length of marriages are given and finally Laplace looks at moral expectation and probability in legal matters.
    • Much of this work was done by Laplace between 1817 and 1819 and appears in the 1820 edition of the Theorie Analytique Ⓣ.
    • This final supplement was presented to the Institute by Laplace, who was 76 years old by this time, and by his son.
    • We mentioned briefly above Laplace's first work on physics in 1780 which was outside the area of mechanics in which he contributed so much.
    • Around 1804 Laplace seems to have developed an approach to physics which would be highly influential for some years.
    • This is best explained by Laplace himself:- .
    • It is worth remarking that it was a new approach, not because theories of molecules were new, but rather because it was applied to a much wider range of problems than any previous theory and, typically of Laplace, it was much more mathematical than any previous theories.
    • Laplace's desire to take a leading role in physics led him to become a founder member of the Societe d'Arcueil in around 1805.
    • The group strongly advocated a mathematical approach to science with Laplace playing the leading role.
    • This marks the height of Laplace's influence, dominant also in the Institute and having a powerful influence on the Ecole Polytechnique and the courses that the students studied there.
    • After the publication of the fourth volume of the Mecanique Celeste Ⓣ, Laplace continued to apply his ideas of physics to other problems such as capillary action (1806-07), double refraction (1809), the velocity of sound (1816), the theory of heat, in particular the shape and rotation of the cooling Earth (1817-1820), and elastic fluids (1821).
    • Arago, who had been a staunch member of the Society, began to favour the wave theory of light as proposed by Fresnel around 1815 which was directly opposed to the corpuscular theory which Laplace supported and developed.
    • Many of Laplace's other physical theories were attacked, for instance his caloric theory of heat was at odds with the work of Petit and of Fourier.
    • However, Laplace did not concede that his physical theories were wrong and kept his belief in fluids of heat and light, writing papers on these topics when over 70 years of age.
    • At the time that his influence was decreasing, personal tragedy struck Laplace.
    • The child, however, survived and it is through her that there are descendants of Laplace.
    • Laplace's son, Charles-Emile, lived to the age of 85 but had no children.
    • Laplace had always changed his views with the changing political events of the time, modifying his opinions to fit in with the frequent political changes which were typical of this period.
    • In 1814 Laplace supported the restoration of the Bourbon monarchy and cast his vote in the Senate against Napoleon.
    • On the morning of Monday 5 March 1827 Laplace died.
    • Surprisingly there was no quick decision to fill the place left vacant on his death and the decision of the French Academy of Sciences in October 1827 not to fill the vacant place for another 6 months did not result in an appointment at that stage, some further months elapsing before Puissant was elected as Laplace's successor.
    • A Poster of Pierre-Simon Laplace .
    • Laplace's Mechanique Celeste/a> .
    • Laplace on "new stars" .
    • Laplace: Essay on probabilities .
    • Charles Babbage on Laplace Fourier and Biot .
    • Honours awarded to Pierre-Simon Laplace .
    • 3.nLunar featuresnPromontorium Laplace .
    • 4.nParis street namesnRue Laplace (5th Arrondissement) .
    • .

  2. Jean-Baptiste Biot (1774-1862)
    • However, he also managed to get support in his career from Laplace.
    • In fact in late 1799 Biot approached Laplace, who had taught him at l'Ecole Polytechnique, and offered to proof-read the Mecanique celeste Ⓣ which at that time was with the publisher.
    • He did not give up when Laplace said "No thanks" but persisted in a polite way and eventually Laplace agreed.
    • From that time on, each time I went to Paris I brought my proof-reading work and personally presented it to M Laplace.
    • Laplace was also interested in the research on mathematics which Biot was undertaking and gave him advice both on the material and on getting it published.
    • In 1800 he was appointed Professor of Mathematical Physics at the College de France, an appointment which was due mainly to the influence of Laplace.
    • Again Laplace's support was important to Biot in this election.
    • In 1806, again with the support of Laplace, Biot was appointed as an assistant astronomer at the Bureau de Longitudes in addition to his other roles.
    • Among his other major works we mention: Analyse de la mecanique celeste de M Laplace Ⓣ (1801); Traite analytique des courbes et des surfaces du second degre Ⓣ (1802); Recherches sur l'integration des equations differentielles partielles et sur les vibrations des surfaces Ⓣ (1803); Essai de geometrie analytique applique aux courbes et aux surfaces de second ordre Ⓣ (1806); Recherches experimentales et mathematiques sur les mouvements des molecules de la lumiere autour de leur centre de gravite Ⓣ (1814); Traite de physique experimentale et mathematique Ⓣ (1816); Precis de physique Ⓣ (1817); (with Arago) Recueil d'observations geodesiques, astronomiques et physiques executees en Espagne et Ecosse Ⓣ (1821); Memoire sur la vraie constitution de l'atmosphere terrestre Ⓣ (1841); Traite elementaire d'astronomie physique Ⓣ (1805); Recherches sur plusieurs points de l'astronomie egyptienne Ⓣ (1823); Recherches sur l'ancienne astronomie chinoise Ⓣ (1840); Etudes sur l'astronomie indienne et sur l'astronomie chinoise Ⓣ (1862); Essai sur l'histoire generale des sciences pendant la Revolution Ⓣ (1803); Discours sur Montaigne Ⓣ (1812); Lettres sur l'approvisionnement de Paris et sur le commerce des grains Ⓣ (1835); Traite d'astronomie physique Ⓣ (1850); and Melanges scientifiques et litteraires Ⓣ (1858).
    • Charles Babbage on Laplace Fourier and Biot .

  3. Henri Andoyer (1862-1929)
    • For example there is A propos de l'Almageste de Ptolemee Ⓣ (1928), A propos des oeuvres de Copernic Ⓣ (1928), (with Pierre Humbert) Histoire des Sciences en France, Mathematique, Mechanique, Astronomie Ⓣ, and L'Oeuvre scientifique de Laplace Ⓣ (1922).
    • Florian Cajori writes in a review about this last mentioned work [',' F Cajori, Review: L’Oeuvre scientifique de Laplace, by Henri Andoyer, Bull.
    • After a brief sketch of the life of Laplace, Andoyer sets forth the characteristics of the works of this great French scientist.
    • Andoyer presents evidence showing the excessive harshness of the judgment passed upon Laplace by certain writers, to the effect that Laplace, in his writings, often failed to give due credit to his predecessors and contemporaries.
    • Laplace's relations to D'Alembert, Biot and Poisson are described.
    • Andoyer explains how Laplace again and again returned to certain topics in order that he might improve his exposition and perhaps free the subject from metaphysical entanglements.
    • Not altogether surprising is Laplace's lack of interest in certain abstract fields of mathematics, like the theory of numbers.
    • But strange is Laplace's adherence to Newton's corpuscular theory of light a quarter of a century after Thomas Young had advocated the undulatory theory and a decennium after Fresnel had won Arago over to the latter theory.
    • Andoyer's masterly account of Laplace's researches on celestial mechanics, on the figure of the earth, on the tides, on the systeme du monde, on the analytical theory of probability, and of researches on physics contains numerous quotations from the works of Laplace, bearing on points of scientific and philosophical interest.

  4. Joseph Fourier (1768-1830)
    • and also by Laplace, who Fourier rated less highly, and by Monge who Fourier described as .
    • Fourier began teaching at the College de France and, having excellent relations with Lagrange, Laplace and Monge, began further mathematical research.
    • His release has been put down to a variety of different causes, pleas by his pupils, pleas by Lagrange, Laplace or Monge or a change in the political climate.
    • The memoir was read to the Paris Institute on 21 December 1807 and a committee consisting of Lagrange, Laplace, Monge and Lacroix was set up to report on the work.
    • The first objection, made by Lagrange and Laplace in 1808, was to Fourier's expansions of functions as trigonometrical series, what we now call Fourier series.
    • All these are written with such exemplary clarity - from a logical as opposed to calligraphic point of view - that their inability to persuade Laplace and Lagrange ..
    • Laplace, and later Poisson, had similar objections.
    • Only one other entry was received and the committee set up to decide on the award of the prize, Lagrange, Laplace, Malus, Hauy and Legendre, awarded Fourier the prize.
    • Charles Babbage on Laplace Fourier and Biot .

  5. Aldo Ghizzetti (1908-1992)
    • He was strongly influenced by Guido Fubini and, at Fubini's suggestion, he began to study the theory of Laplace transformations in particular looking to use the technique in applications to electrical engineering.
    • He published Sull'uso della trasformazione di Laplace nello studio dei circuiti elettrici Ⓣ (1937), and La trasformazione di Laplace e il calcolo simbolico degli elettrotecnici Ⓣ(1941) which provided an expository representation of the symbolic calculus of electric circuit theory based on the Laplace transformation.
    • La Trasformazione di Laplace e il Calcolo Simbolico degli Elettrotecnici Ⓣ (1943).
    • The aim of this monograph is to supply a treatment of the Laplace transform and its applications to electric circuit theory.
    • Part one provides an elementary discussion of the unilateral Laplace transform.
    • This new work, entitled Trasformate di Laplace e calcolo simbolico Ⓣ was published in 1971.

  6. Siméon-Denis Poisson (1781-1840)
    • His teachers Laplace and Lagrange quickly saw his mathematical talents.
    • He proceeded immediately to the position of repetiteur in the Ecole Polytechnique, mainly on the strong recommendation of Laplace.
    • His first attempt to be elected to the Institute was in 1806 when he was backed by Laplace, Lagrange, Lacroix, Legendre and Biot for a place in the Mathematics Section.
    • In the first Sur les inegalites des moyens mouvements des planetes Ⓣ he looked at the mathematical problems which Laplace and Lagrange had raised about perturbations of the planets.
    • It also marked a move away from experimental research towards theoretical research in what was considered to constitute physics, and in this the Institute was following the lead given by Laplace.
    • Much of Poisson's work was motivated by results of Laplace, in particular his work on the relative velocity of sound and his work on attractive forces.
    • This latter work was not only influenced by Laplace's work but also by the earlier contributions of Ivory.
    • Lagrange and Laplace recognised Fermat as the inventor of the differential and integral calculus; he was French after all, while neither Leibniz nor Newton were! Poisson, however, wrote in 1831:- .

  7. Nathaniel Bowditch (1773-1838)
    • On his voyage of 1802-03 he read the first volume of Laplace's Traite de mecanique celeste which had been published in 1798.
    • By June 1806 Bowditch had read the first four of Laplace's five volumes (the fifth volume was not published by Laplace until 1825).
    • Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste was completed by 1818 but he would not publish it for many years.
    • to supply steps omitted in the original text; to incorporate later results into the translation; and to give credits omitted by Laplace.
    • As president of the Massachusetts Hospital Life Insurance Company, he enjoyed enough material success so that he could afford the $12,000 it cost to have his translation of Laplace published (1829-1839).
    • (Bronx, N.Y., 1969).','4] which is a reprint of the French original of Laplace's fifth volume.
    • Laplace's Mechanique Celeste .

  8. Giovanni Plana (1781-1864)
    • This episode is described in detail in [',' G Tagliaferri and P Tucci, Carlini and Plana on the theory of the moon and their dispute with Laplace, Ann.
    • In 1818 Laplace proposed that the Academie des Sciences in Paris set up a prize to be awarded to whoever succeeded in constructing lunar tables based solely on the law of universal gravity.
    • In 1820 the prize was awarded to Carlini and Plana and to Damoiseau by a committee of which Laplace was a member.
    • But Laplace strongly criticised the Carlini-Plana approach to lunar theory.
    • letters [were] exchanged between Carlini-Plana and Laplace, and ..
    • After the exchanges, public and private, between Carlini-Plana and Laplace, the latter concluded that the results of the Italian astronomers and those arrived at by Damoiseau following the method of Laplace's 'Mecanique celeste' were fairly close, and that the purpose of the Academie in establishing the prize had been reasonably fulfilled.

  9. Jules Bienaymé (1796-1878)
    • In fact the jury system in France at that time was based on Laplace's conclusions but it was under attack by Poisson.
    • Bienayme supported Laplace on this issue.
    • In fact Bienayme supported Laplace in general since it was Laplace's Theorie analytique des probabilites Ⓣ (1812) that was the biggest influence on Bienayme's scientific thinking throughout his life.
    • One of his many contributions was to generalise the Laplace method of least squares - in fact much of his work can be thought of as extending and generalising ideas introduced by Laplace.
    • Bienayme published the Bienayme-Chebyshev inequality, which was used to give a very simple and precise demonstration of the generalised law of large numbers, in his important paper Considerations a l'appui de la decouverte de Laplace sur la loi de probabilite dans la methode des moindres carres Ⓣ (1853).

  10. Charles Eugène Delaunay (1816-1872)
    • Mme la Marquise de Laplace donated a new annual prize, the Laplace Prize, to be given to the student who was ranked top in his year at the Ecole Polytechnique.
    • Delaunay had graduated before the prize was instituted but Mme de Laplace requested that he become the first recipient of the prize which consisted of the complete works of Laplace.
    • It turned out to be a decision which changed the course of Delaunay's career, for reading Laplace's great works gave him a passion for celestial mechanics and he decided that he would make a career in that subject.
    • Mme la Marquise de Laplace was delighted with the first winner of the prize and she called him "her eldest son".

  11. Semyon Aranovich Gershgorin (1901-1933)
    • The papers he published at this time are (all in Russian): Instrument for the integration of the Laplace equation (1925); On a method of integration of ordinary differential equations (1925); On the description of an instrument for the integration of the Laplace equation (1926); and On mechanisms for the construction of functions of a complex variable (1926).
    • Gershgorin proposed an original and intricate mechanism for solving the Laplace equation, and he described such a device in detail in 'Instrument for the integration of the Laplace equation' (1925).
    • In 1929 Gershgorin published On electrical nets for approximate solution of the differential equation of Laplace (Russian) in which he gave a method for finding approximate solutions to partial differential equations by constructing a model based on networks of electrical components.
    • In the following year he published Fehlerabschatzung fur das Differenzverfahren zur Losung partieller Differentialgleichungen Ⓣ in which he made a careful analysis of the convergence of finite-difference approximation methods for solving the Laplace equation.

  12. Józeph Petzval (1807-1891)
    • During his two years at the university he studied the works of Lacroix, Laplace and Lagrange.
    • Petzval worked for much of his life on the Laplace transform.
    • He was influenced by the work of Liouville and wrote both a long paper and a two volume treatise on the Laplace transform and its application to ordinary linear differential equations.
    • But for a student of Petzval we might today call the Laplace transform the Petzval transform.
    • Petzval fell out with this student who then accused Petzval of plagiarising Laplace's work.
    • Although this was untrue, George Boole and Henri Poincare, influenced no doubt by the quarrel, called the transformation the Laplace transform.

  13. Simon Newcomb (1835-1909)
    • He was able to borrow a copy of Bowditch's translation of Laplace's Mecanique celeste from the library of the Smithsonian Institution but found that the mathematics which the book contained was rather beyond his current knowledge.
    • Laplace had devised a method involving cosine series for computing the perturbing force on a planet caused by other planets.
    • The coefficients in the series were known as 'Laplace coefficients' but the drawback of the method was that it only worked for circular orbits.
    • Newcomb showed how to extend Laplace's series to give a perturbing function in the case of elliptical orbits by introducing differential operators which act on the Laplace coefficients.

  14. William Ferrel (1817-1891)
    • He sent to Philadelphia for a copy of Bowditch's translation of Laplace's Mecanique Celeste which he also studied.
    • This conclusion contradicted that which Laplace had come to and Ferrel decided that Laplace had made an error in neglecting second order terms.
    • We have seen above how Ferrel's early work on tides sought to correct some problems which were in Laplace's treatment.
    • When Laplace studied the tides he had ignored fluid friction because no good mathematical treatment existed at that time.

  15. Harry Bateman (1882-1946)
    • My own interest in the integrals of the Euler-Laplace type dates, I think, from the time when Sir Edmund Whittaker gave some properties of the Laplace transformation in his lectures at Cambridge in 1903 or 1904.
    • I made some use of the method of the inverse Laplace transformation in the Smith's prize essay and fellowship dissertation partly published in modified form in 1909 and 1910.
    • Bateman was one of the first to apply Laplace transforms to integral equations in 1906.
    • Bateman's method was the now familiar one of applying the complex inversion formula of the Laplace transform.

  16. James Ivory (1765-1842)
    • During these years he had spent much of his spare time in studying the works of Lagrange and Laplace on his own.
    • Ivory and Wallace were early supporters of the work of the French analysts, especially Lagrange and Laplace.
    • Ivory's critical commentary of Laplace's Mecanique celeste was praised by Laplace.
    • His work on the ellipsoidal equilibrium configuration of self-gravitating fluids was an extension of that of Laplace, and it influenced the achievements of Jacobi and Liouville which followed.

  17. Richard Price (1723-1791)
    • In [',' S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.
    • Zabell [',' S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.
    • This is not Laplace's rule of succession, but rather a calculation of the posterior probability that the unknown chance x of the event exceeds 1/2, based on Bayes's assumption that all values of x are a priori equally likely.
    • On the forenoon of the 4th of November [',' Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.

  18. Mary Somerville (1780-1872)
    • At this time Mary also read Newton's Principia and, at Wallace's suggestion, Laplace's Mecanique Celeste and many other mathematical and astronomical texts.
    • Mary met Laplace, Poisson, Poinsot, Emile Mathieu and many others.
    • In 1827 Lord Brougham made a request on behalf of the Society for the Diffusion of Useful Knowledge for Mary Somerville to translate Laplace's Mecanique Celeste.
    • However Mary went far beyond a translation, for she explained in detail the mathematics used by Laplace which was unfamiliar to most mathematicians in England at that time.

  19. John Couch Adams (1819-1892)
    • Adams spent much effort on the complex problem of a description of the motion of the Moon, giving a theory which was more accurate than that of Laplace.
    • He began this work in 1851 when elected as President of the Royal Astronomical Society and he presented a paper to the Royal Society in 1853 in which he showed that Laplace had omitted terms from his equations which were not negligible.
    • His corrections to Laplace's work reduced by half the discrepancy between the observed orbit and the predicted one.
    • It is fair to say that the French were not pleased to see Adams correcting Laplace, particularly since they had reacted angrily a few years earlier when they saw him as attempting to detract from Le Verrier's glory.

  20. Robert Adrain (1775-1843)
    • In this paper Adrain gave 1/319 as the ellipticity of the Earth, a figure better than that given by Laplace (he gave 1/336), and about halfway between Laplace's figure and the accepted value today of 1/297.
    • Adrain's improvement on Laplace's value was, of course, made because Adrain had been inspired to work on the topic because of the contributions of Laplace.

  21. Adrien-Marie Legendre (1752-1833)
    • From 1775 to 1780 he taught with Laplace at Ecole Militaire where his appointment was made on the advice of d'Alembert.
    • He wrote to Laplace asking for more information about the prize winning young mathematician.
    • Legendre submitted his results to the Academie des Sciences in Paris in January 1783 and these were highly praised by Laplace in his report delivered to the Academie in March.
    • Within a few days, on 30 March, Legendre was appointed an adjoint in the Academie des Sciences filling the place which had become vacant when Laplace was promoted from adjoint to associe earlier that year.

  22. Jean-Baptiste-Joseph Delambre (1749-1822)
    • At the same meeting Laplace presented a paper on his mathematical results which allowed the perturbations produce by one planet on the orbit of another to be calculated.
    • Delambre was very impressed and decided to make observations of the orbit of Uranus in order to verify Laplace's theoretical results.
    • The topic had been suggested by Laplace and Lalande with Delambre in mind, and the committee consisting of Dominique Cassini, Lalande and Mechain duly awarded him the prize, declaring him to be:- .
    • The Academie had already set up a Commission of Weights and Measures in 1790 consisting of Borda, Condorcet, Laplace, Legendre and Lavoisier to advise on a metric system of weights and measures.

  23. François Arago (1786-1853)
    • Laplace asked Poisson to find someone who would continue the work, and Poisson proposed his young friend Arago.
    • We should also note that he used his political positions to advance science, such as obtaining money to fund the publication of the works of Fermat and Laplace, supporting the development of railways and of the telegraph.
    • Arago smiled at the beautiful experiment [of Fizeau and Foucault] which, with its well deserved praise, brought back pleasant memories of his own glory days when he beat Laplace, Poisson, and Biot, to gain his place in the Academy of Sciences.

  24. Ugo Amaldi (1875-1957)
    • On 28 November 1898 Amaldi graduated after submitting a thesis on the Laplace transform entitled La trasformazione di Laplace e le equazioni differenziali lineari, a coefficienti razionali, di rango 1 Ⓣ.
    • While collaborating with Pincherle on writing a treatise, Amaldi published Sulla trasformazione di Laplace Ⓣ (1898) and Sulle sostituzioni lineari commutabili Ⓣ.

  25. Johann Karl Burckhardt (1773-1825)
    • He made the decision to go to Paris because working for Lalande he would have as his assistants other competent astronomers who had been pupils of Lagrange, Laplace and Lalande.
    • He translated the first two volumes of Laplace's 'Mecanique celeste' Ⓣ while reading the proofs; he also added some notes and double checked the calculations, made by Alexis Bouvard.
    • The Bureau des Longitudes had to chose the best lunar tables for their astronomical almanac, the Connaissance des Temps Ⓣ, so they appointed a committee consisting of Laplace, Delambre, Bouvard, Arago and Poisson to compare Burckhardt's tables with those of Johann Tobias Burg, an astronomer working in Vienna, that were the most accurate available at the time.

  26. Alonzo Church (1903-1995)
    • For example he published Remarks on the elementary theory of differential equations as area of research in 1965 and A generalization of Laplace's transformation in 1966.
    • The paper includes a discussion of a generalization the Laplace transform which he extends to non-linear partial differential equations.
    • This generalization of the Laplace transform is the topic of study of the second paper, again using the method to obtain solutions of second-order partial differential equations.

  27. Georges Darmois (1888-1960)
    • He published four papers between 1910 and 1914: Sur les correspondances a normales concourantes Ⓣ (1910); Sur les courbes algebriques a torsion constante Ⓣ (1913); Sur les courbes a torsion constante Ⓣ (1914); and Sur la methode de Laplace Ⓣ (1914).
    • Equally simple is the presentation of pairs of variables with the corresponding Laplace-Gauss law, convergence theorems, domains of attraction of the Laplace-Gauss law, with elements of the theory of errors and the influence of dependence on random quantities.

  28. Joseph-Louis Lagrange (1736-1813)
    • He decided to write a definitive work incorporating his contributions and wrote to Laplace on 15 September 1782:- .
    • It had been approved for publication by a committee of the Academie des Sciences comprising of Laplace, Cousin, Legendre and Condorcet.
    • The weights and measures commission was the only one allowed to continue and Lagrange became its chairman when others such as the chemist Lavoisier, Borda, Laplace, Coulomb, Brisson and Delambre were thrown off the commission.

  29. Gustav Doetsch (1892-1977)
    • Also in the 1920s Doetsch collaborated with Felix Bernstein on what is considered today to be the modern version of the Laplace transform.
    • Doetsch had collaborated with a number of Jewish mathematicians; his doctoral supervisor was Edmund Landau and his collaborator on the Laplace transform was Felix Bernstein, both Jewish mathematicians.
    • His most important mathematical contribution during this time was his major text on the Laplace transform and its applications to engineering published in 1937, the first such text to be written.

  30. Alexis Bouvard (1767-1843)
    • In 1794 Bouvard met Laplace who was at that time working on his great masterpiece Mechanique celeste Ⓣ.
    • Laplace recognised Bouvard's computing skills and soon had him carrying out the complex calculations required for his theory.
    • Realising Bouvard's potential, Laplace arranged for him to be offered a position in the important Bureau de longitudes in 1794.

  31. Pafnuty Chebyshev (1821-1894)
    • Legendre and Laplace had encountered the Legendre polynomials in their work on celestial mechanics in the late eighteenth century.
    • Laplace had found and studied the Hermite polynomials in the course of his discoveries in probability theory during the early nineteenth century.
    • Twenty years later Chebyshev published On two theorems concerning probability which gives the basis for applying the theory of probability to statistical data, generalising the central limit theorem of de Moivre and Laplace.

  32. Horatio Carslaw (1870-1954)
    • 24 (1) (1997), 4-16.','4] claims it to be his later work on Laplace transforms.
    • The fact that Jaeger himself collaborated with Carslaw on the Laplace transform work may explain why there are differing opinions here.
    • In 1935, the Laplace transform was a topic of frontline research, by 1955 it was standard fare in undergraduate courses.

  33. Benjamin Peirce (1809-1880)
    • Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste Ⓣ had been completed by 1818 but he had still not published it during the years that Peirce was an undergraduate.
    • The course he set up was impressive, including the study of works of Lacroix, Cauchy, Monge, Biot, Hamilton, Laplace, Poisson, Gauss, Le Verrier, Bessel, Adams, Airy, MacCullagh and Franz Neumann.
    • He also revised and wrote a commentary on Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste which he had himself had proof-read as an undergraduate student.

  34. Ian Sneddon (1919-2000)
    • The book discusses applications of Fourier, Mellin, Laplace and Hankel transforms to the solution of problems in physics and engineering.
    • It does not confine itself merely to the Laplace transform, and many of the applications are of a more advanced nature than is usual - the later chapters are based almost entirely on work published within the last ten years.
    • The book deals with, among other topics, Laplace's equation, mixed boundary value problems, the wave equation, and the heat equation.

  35. Augustin-Louis Cauchy (1789-1857)
    • Laplace and Lagrange were visitors at the Cauchy family home and Lagrange in particular seems to have taken an interest in young Cauchy's mathematical education.
    • He took a copy of Laplace's Mecanique Celeste Ⓣ and one of Lagrange's Theorie des Fonctions Ⓣ with him.

  36. Adolphe Quetelet (1796-1874)
    • He learnt astronomy from Arago and Bouvard and the theory of probability under Joseph Fourier and Pierre Laplace.
    • Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law.

  37. Pierre Méchain (1744-1804)
    • The Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, was set up by the Academie des Sciences in 1790 to bring in a uniform system of measurement.
    • Napoleon, after taking advice from Delambre and Laplace, approved the mission.

  38. Patrick Keast (1942-2016)
    • It is the purpose of this note to demonstrate this fact, and also to discuss the solution of Laplace's and Poisson's equations, when the Laplacian operator is singular, in a sense to be defined.
    • It will be shown that, for certain boundary conditions, the numerical solution of Laplace's equation is best obtained by direct methods, rather than by iterative methods.

  39. Alessandro Faedo (1913-2001)
    • Faedo published several papers in 1940-41 on a variety of different topics: Il principio di Zermelo per gli spazi astratti Ⓣ (1940), Sulle trasformate multiple di Laplace (1941); Contributo alla sistemazione teorica del metodo variazionale per l'analisi dei problemi di propagazione Ⓣ (1941), Su gli insiemi chiusi di misura nulla Ⓣ (1941), and Il principio di Zermelo per lo spazio delle funzioni continue Ⓣ (1941).
    • We have already seen that he made contributions to a wide variety of areas such as the calculus of variations, the theory of linear ordinary differential equations, the theory of partial differential equations, measure theory, the Laplace transform for functions of several variables, questions relating to existence for linear equations in Banach spaces, and foundational problems such as his work on Zermelo's principle in infinite-dimensional function spaces.

  40. Henri Garnir (1921-1985)
    • He worked on distribution theory, publishing an important paper Sur la transformation de Laplace des distributions Ⓣ (1952).
    • In this paper he initiated the study of Laplace transformations in distribution theory.

  41. Francis Murnaghan (1893-1976)
    • After he retired from his position in Brazil and returned to the United States he published The calculus of variations and The Laplace transformation , both in 1962.
    • The first of these is a short book of less that 100 pages written for engineers and scientists, while the second consists of 19 lectures on such topics as: the Fourier integral; the Laplace integral transformation; the differential equations of Laguerre and Bessel; properties of special functions; asymptotic series for an error function, and for certain Bessel functions.

  42. Agnes Mary Clerke (1842-1907)
    • She wrote famous biographies of Galileo, Huygens, Kepler, Lagrange, Laplace, and other scientists for the ninth edition of Encyclopaedia Britannica.
    • The article on Laplace is particularly interesting since it discusses his mathematics in considerable depth.

  43. Sheila Scott Macintyre (1910-1960)
    • The Laplace transformation was applied here, as it had been by various previous writers on the theory of functions, notably by A J Macintyre.
    • Mrs Macintyre later devised an integral transform in which the kernel was obtained from that of the Laplace transform by a process involving fractional differentiation, and applied it to extend the theory of the Gregory-Newton and Abel interpolation series.

  44. Victor Puiseux (1820-1883)
    • In it he investigated questions which had been examined earlier by Laplace, Lagrange and Poisson.
    • Laplace's theory of the Moon, presented in 1787, had been shown to be inadequate by Adams in 1853.

  45. James Serrin (1926-2012)
    • Since its first applications in the study of the Laplace and linear elliptic operators in general, the maximum principle has found a wide range of applications in nonlinear partial differential equations and inequalities, including equations involving the celebrated p-Laplace operator.

  46. Karl Maruhn (1904-1976)
    • During these years as a school teacher he was very active in research publishing the papers: Uber den Laplaceschen Ringkorper Ⓣ (submitted from Leipzig on 26 January 1932), Uber den von Laplace postulierten Urkorper Ⓣ (submitted from Leipzig on 6 January 1933), Uber einige Gleichgewichtsfiguren rotierender Flussigkeiten, auf deren Oberflachen singulare Punkte liegen Ⓣ (submitted from Leipzig on 17 November 1933), Uber zwei Gleichgewichtsfiguren rotierender inhomogener Flussigkeit Ⓣ (submitted from Leipzig on 14 April 1934), and Uber die Verzweigung der Losung einer Integro-Differentialgleichung aus der Theorie der Gleichgewichtsfiguren rotierender Flussigkeiten Ⓣ (submitted from Leipzig on 30 October 1934).
    • In this last mentioned paper, Maruhn reminds the reader that the solutions of the boundary value problems for Laplace's equation are not unique when the boundary functions are allowed to assume infinite values.

  47. Jean-Charles de Borda (1733-1799)
    • When Borda was made Chairman of the Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, he soon put his accurate surveying instrument to good use.
    • In early 1793 it looked as though political events would prevent the project being completed and Borda, Lagrange and Laplace made a provisional estimate of the metre based on a survey previously carried our by Cassini de Thury.

  48. George Jeffery (1891-1957)
    • He did one years teacher training in 1911 but he was already undertaking research and his first paper On a form of the solution of Laplace's equation suitable for problems relating to two spheres was read to the Royal Society in 1912.
    • He made effective use of Whittaker's general solution to Laplace's equation which Whittaker found in 1903.

  49. Claude-Louis Mathieu (1783-1875)
    • Mathieu was one of the two enthusiasts who did most to have the legislation to revive the metric system brought in, the other being Charles-Emile Laplace, the son of Pierre-Simon Laplace.

  50. Balthasar van der Pol (1889-1959)
    • Let us look first at the last of these topics on which Bremmer and van der Pol collaborated in writing the classic text Operational Calculus: Based on the Two-Sided Laplace Integral.
    • This 1950 book was not the first joint work of van der Pol and Bremmer on the operational calculus, for example they published two papers with the title Modern operational calculus based on the two-sided Laplace integral in 1948.

  51. Georg Simon Ohm (1789-1854)
    • Langsdorf, however, advised Ohm to continue with his studies of mathematics on his own, advising Ohm to read the works of Euler, Laplace and Lacroix.
    • As he had done for so much of his life, Ohm continued his private studies reading the texts of the leading French mathematicians Lagrange, Legendre, Laplace, Biot and Poisson.

  52. Achille-Pierre Dionis du Séjour (1734-1794)
    • However, he wrote extensively on applications of mathematics to astronomy, in particular planetary orbits, and his work was highly regarded by Lagrange, Laplace and Condorcet.
    • With Condorcet and Laplace he undertook a determination of the population of France [',' R Taton, Biography in Dictionary of Scientific Biography (New York 1970-1990).

  53. George Green (1793-1841)
    • He translated the first volume of Laplace's Mecanique celeste into English and he published this in Nottingham in 1814.
    • Among them are Cavendish's single-fluid theoretical study of electricity of 1771, two memoirs by Poisson of 1812 on surface electricity and three on magnetism (1821-1823), and contributions by Arago, Laplace, Fourier, Cauchy, and T Young.

  54. John Herschel (1792-1871)
    • These trips included visits to other scientist, for example while in Paris Herschel and Babbage had discussed topics of common interest with Arago, Laplace and Biot.
    • Biot considered him the natural successor to Laplace when he died in 1827.

  55. Aleksei Krylov (1863-1945)
    • In 1931 he found a new method of solving the secular equation determining the frequency of vibrations in mechanical systems which is better than methods due to Lagrange, Laplace, Jacobi and Le Verrier.
    • Before we describe these methods, it is good to return a bit back and consider how the first creators of these methods, Lagrange and Laplace, and then such a great astronomer as Le Verrier and such a great mathematician as Jacobi proceeded ..

  56. Thomas Bayes (1702-1761)
    • Bayes's conclusions were accepted by Laplace in a 1781 memoir, rediscovered by Condorcet (as Laplace mentions), and remained unchallenged until Boole questioned them in the Laws of Thought .

  57. Jean-Nicolas Nicollet (1786-1843)
    • At the Observatory he continued his education, studying under Laplace.
    • Nicollet had lost his patron when Laplace died in 1827 and he had quarrelled with Francois Arago who was becoming an increasingly important figure at the Observatory.

  58. Lejeune Dirichlet (1805-1859)
    • He had some of the leading mathematicians as teachers and he was able to profit greatly from the experience of coming in contact with Biot, Fourier, Francoeur, Hachette, Laplace, Lacroix, Legendre, and Poisson.
    • He turned to Laplace's problem of proving the stability of the solar system and produced an analysis which avoided the problem of using series expansion with quadratic and higher terms disregarded.

  59. Pietro Paoli (1759-1839)
    • His contributions show that he possessed a deep knowledge of the works of Lagrange, Laplace and Monge.
    • Among Paoli's publications we mention Liburnensis Opuscula analytica Ⓣ (1780), Ricerche sulle serie Ⓣ (1788) which corrects an error in a 1779 paper by Laplace on series, Della integrazione dell'equazioni a differenze parziali finite ed infinitesime Ⓣ (1800), Sulle oscillazioni di un corpo pendente da un filo estendibile memoria Ⓣ(1815), and Sull'uso del calcolo delle differenze finite nella dottrina degl'integrali definiti memoria Ⓣ (1828).

  60. John T Graves (1806-1870)
    • Hamilton had studied Clairaut's Algebra, Laplace's Mecanique Celeste and Newton's Principia before entering Trinity College.
    • Bartholomew Lloyd had become professor of mathematics at Trinity in 1813 and, taking over a department in which the teaching had been very old-fashioned with no calculus taught, he had quickly introduced the continental approach to calculus teaching from Lacroix's textbook Traite elementaire de calcul differentiel et du calcul integral, from Poisson's Traite de mecanique, and from Laplace's Mecanique Celeste.

  61. William Rowan Hamilton (1805-1865)
    • At age 15 he started studying the works of Newton and Laplace.
    • In 1822 Hamilton found an error in Laplace's Mecanique celeste and, as a result of this, he came to the attention of John Brinkley, the Royal Astronomer of Ireland, who said:- .

  62. William Thomson (1824-1907)
    • In particular the works of Lagrange, Laplace, Legendre, Fresnel and Fourier were treated with "reverence" to use a word which Thomson himself would later use to describe the attitude that his lecturers had towards these French mathematicians.
    • In fact Thomson also read Laplace's Mecanique celeste in session 1839-40 and visited Paris during this session.

  63. André-Marie Ampère (1775-1836)
    • Laplace noticed an error, explaining the error to Ampere in a letter, which Ampere was able to correct and the treatise was reprinted.
    • By 1816 he was a strong advocate of a wave theory of light, agreeing with Fresnel and opposed to Biot and Laplace who advocated a corpuscular theory.

  64. Archibald Macintyre (1908-1967)
    • thesis, one finds such topics as asymptotic paths, the flat regions of meromorphic functions, interpolation problems based on the Laplace transform and other formulae for regular functions, Tauberian theorems in connection with certain canonical products, and numerous problems, many published jointly with R Wilson, in the theory of the singularities of f (z) = ∑cn zn on the circle of convergence.

  65. Richard Fuchs (1873-1944)
    • Already the theory of complex variables was being used in the design of aircraft wings and Laplace transforms were heavily used in electrical engineering.

  66. Julius Plücker (1801-1868)
    • It was while he was studying in Paris that Plucker learned the importance of analytical mechanics as developed by Laplace and Lagrange as well as that of geometric mechanics as developed by Poinsot.

  67. John Pratt (1809-1871)
    • He revised the work in 1842, then expanded and republished it under the title On attractions, Laplace's functions and the figure of the Earth in 1860.

  68. Martin Bartels (1769-1836)
    • After graduating in 1811, Lobachevsky remained in Kazan to study with Bartels who guided his reading of Gauss's Disquisitiones Arithmeticae Ⓣ and Laplace's Mecanique Celeste Ⓣ.

  69. Augustin Fresnel (1788-1827)
    • In 1819 the committee to judge the Grand Prix of the Academie des Sciences, with Arago as chairman, and including Poisson, Biot and Laplace, met to consider Fresnel's submission.

  70. Timofei Fedorovic Osipovsky (1765-1832)
    • He also translated Laplace's Mechanique celeste into Russian.

  71. Hermann Grassmann (1809-1877)
    • He took the basic theory from Laplace's Mechanique celeste Ⓣ and from Lagrange's Mechanique analytique Ⓣ but he realised that he was able to apply the vector methods which he had been developing since 1832 (described in the preface to Die Lineale Ausdehnungslehre) to produce an original and simplified approach.

  72. Johann Heinrich Lambert (1728-1777)
    • His contributions to probability are evaluated by Garibaldi and Penco in [',' U Garibaldi and M A Penco, Probability theory and physics between Bernoulli and Laplace : the contribution of J H Lambert (1728-1777) (Italian), in Proceedings of the fifth national congress on the history of physics, Rome, 1984, Rend.

  73. Bruce Kellogg (1930-2012)
    • The results are then applied to similar problems in three dimensions, and the Laplace operator is considered on polyhedral domains with polyhedral interfaces.

  74. Alexandre-Theophile Vandermonde (1735-1796)
    • His friend Monge was also involved with the Ecole Normale as were Lagrange and Laplace.

  75. Jean Chazy (1882-1955)
    • (10) The Laplace equation and the Poisson equation.

  76. Joseph Ritt (1893-1951)
    • Among his heroes were Niels Henrik Abel, Augustin Louis Cauchy, David Hilbert, Carl G J Jacobi, Joseph-Louis Lagrange, the marquis Pierre Simon de Laplace, Joseph Liouville and Jules Henri Poincare.

  77. Jacques-Louis Lions (1928-2001)
    • Evolution: Fourier, Laplace.

  78. Aleksandr Nikolaevich Korkin (1837-1908)
    • He had read, and with his wonderful memory could then recall, most works by Abel, Dirichlet, Euler, Fourier, Gauss, Jacobi, Lagrange, Laplace, Legendre, Monge, and Poisson.

  79. Vladimir A Steklov (1864-1926)
    • In addition to the work for his master's thesis and his doctoral thesis referred to above, he reduced problems to boundary value problems of Dirichlet type where Laplace's equation must be solved on a surface.

  80. Vasilii Sergeevich Vladimirov (1923-2012)
    • The transforms examined include the Fourier transform, the Laplace transform, the Cauchy-Bochner transform, the Hilbert transform and the Poisson transform.

  81. George Boole (1815-1864)
    • At this time Boole was studying the works of Laplace and Lagrange, making notes which would later be the basis for his first mathematics paper.

  82. James Eells (1926-2007)
    • This he did with "Global Analysis" in 1971-72, "Geometry of the Laplace Operator" in 1976-77, and "Partial Differential Equations in Differential Geometry", in 1989-90.

  83. Josif Zakharovich Shtokalo (1897-1987)
    • This book is an introduction to operational calculus, which is based on the theory of the Laplace transformation.

  84. George FitzGerald (1851-1901)
    • He studied the works of Lagrange, Laplace, Franz Neumann, and those of his own countrymen Hamilton and MacCullagh.

  85. Mikhail Fedorovich Subbotin (1893-1966)
    • Subbotin not only showed the possibility of improving the convergence of the trigonometric series by which the behaviour of perturbing forces is represented, but also gave an expression for determining Laplace coefficients and presented formulas for computing the coefficients of the necessary members of the trigonometric series.

  86. Niels Abel (1802-1829)
    • Holmboe was convinced that Abel had great talent and encouraged him greatly taking him on to study the works of Lagrange and Laplace.

  87. Joseph Bertrand (1822-1900)
    • Bertrand mentioned some of his predecessors (De Moivre, Laplace, Bienayme), but did not refer to other scholars, notably to Chebyshev.

  88. Evgenii Mikhailovich Lifshitz (1915-1985)
    • The requirements were: ability to evaluate any indefinite integral (in terms of elementary functions) and to solve any ordinary differential equation of the standard type, knowledge of vector analysis and tensor algebra as well as of principles of the theory of functions of complex variable (theory of residues, Laplace method).

  89. Carlo Cercignani (1939-2010)
    • A few years ago, a collaboration with Sasha Bobylev on self-similar solutions of the Boltzmann equation even led him to a new pretty formula for the inversion of the Laplace transform.

  90. James Pierpont (1866-1938)
    • On the other hand the author, having in mind the needs of the students of applied mathematics, has dwelt at some length on the theory of linear differential equations, especially as regards the functions of Legendre, Laplace, Bessel, and Lame.

  91. Joel E Hendricks (1818-1893)
    • McLean taught Hendricks some interesting mathematics but more than that, he had an excellent mathematics library from which Hendricks was able to borrow and read books such as Charles Hutton's A Course of Mathematics, Isaac Newton's Principia Mathematica, and Nathaniel Bowditch's translation of Laplace's Mecanique Celeste.

  92. Felix Bernstein (1878-1956)
    • His range of interests were remarkable and he worked on convex functions, isoperimetric problems, the Laplace transform, number theory (including Fermat's Last Theorem), differential equations and the mathematical theory of genetics.

  93. Richard Bellman (1920-1984)
    • However he also wrote Analytic number theory (1980), Mathematical methods in medicine (1983), and The Laplace transform (1984).

  94. Harold Jeffreys (1891-1989)
    • In pure mathematics he studied operational methods (where he improved on Heaviside's operational calculus and Laplace transforms), cartesian tensors and asymptotic approximations.

  95. Henri Poincaré (1854-1912)
    • He also showed that series expansions previously used in studying the 3-body problem were convergent, but not in general uniformly convergent, so putting in doubt the stability proofs of Lagrange and Laplace.

  96. Alexander Andreevich Samarskii (1919-2008)
    • was small, about 20 pages of introduction and 20 of content, and was about the study of the perturbation of the discrete spectrum of the Laplace operator with the change of the boundary.

  97. Hermann von Helmholtz (1821-1894)
    • However he did not, rather he studied mathematics on his own, reading works by Laplace, Biot and Daniel Bernoulli.

  98. Salvatore Pincherle (1853-1936)
    • Although his efforts did not prove very fruitful, he was able to study in depth the Laplace transform, iteration problems, and series of generalised factors.

  99. Walter Rudin (1921-2010)
    • Rudin was awarded his doctorate in 1949 for his thesis Uniqueness Theory for Laplace Series.

  100. Charles-François Sturm (1803-1855)
    • As for M Arago, I have two or three times been among the group of scientists he invites to his house every Thursday, and there I have seen the leading scientists, Laplace, Poisson, Fourier, Gay-Lussac, Ampere, etc.

  101. John William Strutt (1842-1919)
    • Among the publications devoted to mathematics, rather than to its applications, are papers on Bessel functions, the relationship between Laplace functions and Bessel functions, and Legendre functions.

  102. Henri Delannoy (1833-1915)
    • In Emploi de l'echiquier pour la resolution de divers problemes de probalilites Ⓣ (1889), Delannoy uses his lattice paths in arrays to solve seven problems already studied by mathematicians such as Ampere, Bertrand, Huygens, Laplace and Rouche.

  103. James Jeans (1877-1946)
    • Jeans' work in fluids led him to believe that Laplace's nebular hypothesis for the creation of the solar system was incorrect.

  104. John Henry Michell (1863-1940)
    • The task of determining the velocity potential is then a boundary-value problem for Laplace's equation ..

  105. Irving Segal (1918-1998)
    • [Hille] suggested that Segal continue his and Tamarkin's investigation of the ideal theory of the algebra of Laplace-Stieltjes transforms absolutely convergent in a fixed half-plane.

  106. Étienne Louis Malus (1775-1812)
    • In 1811 Malus served, along with Lagrange, Legendre, Laplace and Hauy, on the committee to decide on who to award the prize to for the best work on the propagation of heat in solid bodies.

  107. Thomas Hakon Grönwall (1877-1932)
    • Gronwall's work contains classical analysis (Fourier series, Gibbs phenomenon, summability theory, Laplace and Legendre series), differential and integral equations, analytic number theory (transcendental numbers, divisor function, L-function of Dirichlet), complex function theory (Dirichlet L-series, conformal mappings, univalent functions), differential geometry, mathematical physics (problems of elasticity, ballistics, induction, potential theory, kinetic theory of gases, optics), nomography, atomic physics (wave mechanics of hydrogen and helium atom, lattice theory of crystals) and physical chemistry where he is especially known as a very important contributor.

  108. Gheorghe ieica (1874-1939)
    • It describes the work he did on the lattice of mutually conjugated lines on a surface and the Laplace sequence of such lattices [',' K Teleman, On the mathematical work of Gheorghe Tzitzeica, Balkan J.

  109. William Herschel (1738-1822)
    • In 1802 William visited Paris where he met and had discussions with Jerome Lalande, Pierre Mechain, Jean-Baptiste-Joseph Delambre, Pierre-Simon Laplace and Charles Messier.

  110. Mikhail Vasilevich Ostrogradski (1801-1862)
    • These were delivered by Louis Poinsot, Pierre-Simon Laplace, Joseph Fourier, Adrien-Marie Legendre, Simeon-Denis Poisson, Jacques Binet and Augustin-Louis Cauchy.

  111. Matthew O'Brien (1814-1855)
    • In that year he published Mathematical Tracts, Part I, On Laplace's Coefficients, The Figure of the Earth, The Motion of a Rigid Body about its Centre Of Gravity, and Precession and Nutation.

  112. Gabriel Lamé (1795-1870)
    • He used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation.

  113. Humphrey Lloyd (1800-1881)
    • Bartholomew Lloyd had become professor of mathematics at Trinity in 1813 and, taking over a department in which the teaching had been very old-fashioned with no calculus taught, he had quickly introduced the continental approach to calculus teaching from Lacroix's textbook Traite elementaire de calcul differentiel et du calcul integral, from Poisson's Traite de mecanique, and from Laplace's Mecanique Celeste.

  114. Eugène Catalan (1814-1894)
    • This work contained 299 of Catalan's papers, the last paper being Sur une application du theoreme de Bayes, faite par Laplace Ⓣ (August 1888).

  115. Yakov Davydovich Tamarkin (1888-1945)
    • Five papers were published in these journals in 1926 and 1927: On Laplace's integral equations; On Volterra's integro-functional equation; A new proof of Parseval's identity for trigonometric functions; On Fredholm's integral equations, whose kernels are analytic in a parameter; and The notion of the Green's function in the theory of integro-differential equations.

  116. Heinrich Hertz (1857-1894)
    • He was advised by von Jolly to read works of Lagrange, Laplace and Poisson [',' R McCormmach, Biography in Dictionary of Scientific Biography (New York 1970-1990).

  117. Paolo Ruffini (1765-1822)
    • He wrote several works on philosophy, one of which argues against some of Laplace's philosophical ideas.

  118. Benjamin Moiseiwitsch (1927-2016)
    • The second part examines Fourier series and Fourier and Laplace transforms, integral equations, wave motion, heat conduction, tensor analysis, special and general relativity, quantum theory, and variational principles.

  119. John West (1756-1817)
    • These show West to have been familiar with the works of Lagrange, Laplace and Arbogast and, had they been published promptly, would have established him as a leading British exponent of Continental analysis and its applications.

  120. Mauro Picone (1885-1977)
    • Some of his most important books which Picone published during his years in Rome are: Appunti di Analisi superiore Ⓣ (1940), which studies harmonic functions, Fourier, Laplace and Legendre series and the equations of mathematical physics; Lezioni di Analisi funzionale Ⓣ (1946), which concerns the calculus of variations; Teoria moderna dell'integrazione delle funzioni Ⓣ (1946), containing a detailed discussion of the r-dimensional Stieltjes integrals; (with Tullio Viola) Lezioni sulla teoria moderna dell'integrazione Ⓣ (1952), which is basically the previous work by Picone with three extra chapters by Viola; and (with Gaetano Fichera) Trattato di Analisi matematica Ⓣ (Vol 1, 1954, Vol 2, 1955), which puts into a treatise Picone's way of teaching calculus particularly slanted towards the applications studied at the Institute for Applied Calculus.

  121. Alexander Friedmann (1888-1925)
    • In his last year at the University he was working on an essay on the subject I assigned: 'Find all orthogonal substitutions such that the Laplace equation, transformed for the new variables, admits particular solutions in the form of a product of two functions, one of which depends only on one, and the other on the other two variables'.

  122. George Stokes (1819-1903)
    • With Green, who in turn had influenced him, Stokes followed the work of the French, especially Lagrange, Laplace, Fourier, Poisson, and Cauchy.

  123. Urbain Le Verrier (1811-1877)
    • Irritated by the long and recent dominance of the policies of Laplace and Cauchy, Le Verrier argued in effect for a return to Monge's aspirations.

  124. Louis Puissant (1769-1843)
    • On 3 November 1828 Puissant was elected to the Academy of Sciences to fill the vacancy caused by the death of Laplace in the previous year.

  125. Ernst Meissel (1826-1895)
    • Meissel must be judged as a classical mathematician, continuing a tradition from an earlier epoch associated with names like Euler, Laplace, Legendre, Gauss, Jacobi, and Dirichlet.

  126. Sixto Ríos (1913-2008)
    • He submitted his doctoral thesis, La hiperconvergencia de las integrales de Laplace Stieltjes Ⓣ, and was awarded a doctorate on 21 December 1935.

  127. Karl Weierstrass (1815-1897)
    • He did study mathematics on his own, however, reading Laplace's Mecanique celeste Ⓣ and then a work by Jacobi on elliptic functions.

  128. Adegoke Olubummo (1923-1992)
    • He published Left completely continuous B#-algebras (1957), The Laplace-Stieltjes transform of an increasing vector-valued function (1957) and B#-algebras with a certain set of left completely continuous elements (1959).

  129. Charles Augustin Coulomb (1736-1806)
    • Coulomb worked closely with Bossut, Borda, de Prony, and Laplace over this period.

  130. Guido Ascoli (1887-1957)
    • Between 1926 and 1930 he published twelve important works on partial differential equations: these include Sul problema di Dirichlet nei campi sferici e ipersferici Ⓣ (1927); Sulle singolarita isolate delle funzioni armoniche Ⓣ (1928); Sull'unicita della soluzione nel problema di Dirichlet Ⓣ (1928); and Sull'equazione di Laplace dello spazio iperbolico Ⓣ (1929).

  131. Aldo Andreotti (1924-1980)
    • Perhaps his most famous results are his proof of the theorem of Leonida Tonelli (1958), his proof of the duality of Picard and Albanese varieties of algebraic surfaces, his work with A L Mayer on the Schottky problem (1967), and the Andreotti-Vesentini separation theorem which appeared in their joint 1965 paper Carleman estimates for the Laplace-Beltrami equation on complex manifolds.

  132. Louis Benjamin Francoeur (1773-1849)
    • Many of these works were dedicated to famous mathematicians, for example the Elemens de statique Ⓣ was dedicated to Pierre-Simon Laplace, the Geodesie Ⓣ was dedicated to Louis Puissant, and the fifth edition l'Uranographie Ⓣ published in 1837 was dedicated to Francois Arago, the fourth edition of 1828 having been dedicated to Sadi Carnot who died in 1832.

  133. Lazarus Fuchs (1833-1902)
    • As well as attending lectures by the people listed above, Fuchs read Gauss's Disquisitiones arithmeticae and works by Fourier, Laplace and Cauchy.

  134. William Wager Cooper (1914-2012)
    • His legendary partnership with Abraham Charnes has provided results whose connections go back to the 18th century, bearing on problems conceived but left unsolved by Laplace and Gauss.

  135. Ptolemy (about 85-about 165)
    • After comments by Laplace and Lalande, the next to attack Ptolemy vigorously was Delambre.

  136. Erhard Schmidt (1876-1959)
    • We should note, however, that Laplace presented the Gram-Schmidt process before either Gram or Schmidt.

  137. Carl Friedrich Gauss (1777-1855)
    • Gauss used the Laplace equation to aid him with his calculations, and ended up specifying a location for the magnetic South pole.

  138. Aleksandr Osipovich Gelfond (1906-1968)
    • The chapter titles of this book are: Residues; Singular points and series representations of a function; Expansion of a function in a series and properties of the gamma function; Some functional identities and asymptotic estimates; and Laplace transformation and some problems which are solved by the use of residue theory.

  139. Paul Mansion (1844-1919)
    • He wrote on the history of Greek mathematics and on many mathematicians including: Hermite, Abel, de la Vallee Poussin, Saccheri, Lobachevsky, de Tilly, Poincare, Copernicus, Galileo, Kepler, Descartes, Huygens, Leibniz, Newton, d'Alembert, Euler, Laplace, Ampere, Faraday, Quetelet, Lord Kelvin, and Helmholtz.

  140. George Darwin (1845-1912)
    • In particular, using methods introduced by Laplace and Thomson, he discussed the effects of tidal action on the Sun-Earth-Moon system.

  141. Eugenio Beltrami (1835-1900)
    • He gave a generalised form of the Laplace operator.

  142. Jan Mikusiski (1913-1987)
    • This algebraic approach was based on the interpretation of the Laplace convolution as a multiplication in the ring of the continuous functions on the real half-axis.

  143. Claude Berge (1926-2002)
    • The symbolic calculus which he discussed in this major paper is a combination of generating functions and Laplace transforms.

  144. George Hill (1838-1914)
    • These texts included Lacroix' Traite du calcul differentiel et integral, Lagrange's Mechanique analytique, Laplace's Mechanique celeste and Legendre's Fonctions elliptiques.

  145. John Dougall (1867-1960)
    • The author's ingenious proof is based on the repeated application of Laplace's operator to homogeneous harmonic polynomials.

  146. Ruggero Giuseppe Boscovich (1711-1787)
    • Now the young ambitious Laplace attacked his methods.

  147. Stephen Bosanquet (1903-1984)
    • His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961.

  148. Paul Lévy (1886-1971)
    • In 1926 he extended Laplace transforms to broader function classes.

  149. Guglielmo Libri (1803-1869)
    • The following year, being now in the fortunate position of having the title of Professor, being paid a professorial salary but having no commitments, he visited Paris and was well received by the top mathematicians of the day including Laplace, Poisson, Ampere, Fourier and Arago.

  150. Joseph Doob (1910-2004)
    • The first half concerns the potential theory of the Laplace operator (i.e.

  151. Félix Tisserand (1845-1896)
    • Tisserand is especially remembered for his four volume textbook which is an update of Laplace's work.

  152. Gerard Murphy (1948-2006)
    • Murphy discussed recent work on twisted graded traces, an extension of Connes's cyclic cohomology, invariant linear functionals on covariant calculi and the Hodge, Dirac and Laplace operators in this setting.

  153. Joseph Pérès (1890-1962)
    • The next chapter considers the period from Newton to Euler, followed by a chapter covering the period from 1780 to 1860 where Peres looks at the contributions of Lagrange, Laplace, Legendre, Cauchy, Galois, Gauss, Jacobi, Riemann, and Weierstrass.

  154. Edmund Whittaker (1873-1956)
    • His results in partial differential equations (described as 'most sensational' by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation.

  155. Frances Chick Wood (1883-1919)
    • I will not indulge in a rhetoric she detested and proclaim her to be of the fellowship of Laplace, of Galton or of Farr.

  156. Abraham Gelbart (1911-1994)
    • This appears in their joint paper On generalized Laplace transformations (1947).

  157. Jorgen Gram (1850-1916)
    • The process seems to be a result of Laplace and it was essentially used by Cauchy in 1836.

  158. Mineo Chini (1866-1933)
    • Chini taught courses at the University of Pavia from 1898, for example: Geometria infinitesimale delle linee nello spazio e sopra una superficie Ⓣ in the academic year 1899-1900; Teoria della equazione di Laplace Ⓣ in the academic year 1901-1902; and Corso speciale Ⓣ in the academic year 1902-03.

  159. Charles Babbage (1791-1871)
    • Charles Babbage on Laplace Fourier and Biot .

  160. Émile Picard (1856-1941)
    • Starting in 1890, he extended properties of the Laplace equation to more general elliptic equations.

  161. Karl Schwarzschild (1873-1916)
    • His dissertation, on an application of Poincare's theory of stable configurations of rotating bodies to tidal deformation of moons and to Laplace's origin of the solar system, was supervised by Hugo von Seeliger.

  162. Bernard Malgrange (1928-)
    • In the book under review, the author shows how to fully incorporate some new elements of classical analysis and mathematical physics to the theory of D-modules, especially the Laplace and stationary phase methods.

  163. Vijay Patodi (1945-1976)
    • Patodi's first paper Curvature and the eigenforms of the Laplace operator was part of his thesis and the contents of this paper are described in [',' Vijay Kumar Patodi, Geometry and analysis : papers dedicated to the memory of V K Patodi (Bangalore, 1980), i-iii.','2]:- .

  164. Rudolf Clausius (1822-1888)
    • Laplace, Poisson, Sadi Carnot and Clapeyron had all developed the subject using this caloric theory as a basis.

  165. Alexis Petit (1791-1820)
    • The work in which M Laplace has deduced from a rigorous analysis the explanation and the laws of these phenomena, contains, moreover, the solution of several important questions, which depend, by their nature, on the general cause of the capillary effects.

  166. Isaac Todhunter (1820-1884)
    • Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873).

  167. Edward Blades (1875-1953)
    • For example, he communicated On Spheroidal Harmonics and Allied Functions, by Mr G B Jeffery to the meeting on Friday 11 June 1915 and Transformations of Axes for Whittaker's Solution of Laplace's Equation, by Dr G B Jeffery to the meeting on Friday 9 March 1917.

  168. Antoine Cournot (1801-1877)
    • After leaving school he spent four years in a lawyer's office but after he had read Laplace and the correspondence between Leibniz and Clarke he decided to enter university.

  169. Emil Post (1897-1954)
    • It does contain a really important idea, for in the paper Post proves an important result about inverting the Laplace transform.

  170. John Napier (1550-1617)
    • Laplace, 200 year later, agreed, saying that logarithms:- .

  171. Hans Lewy (1904-1988)
    • The solution is given by the sum of two integrals of Laplace type taken over a complex path of integration.

  172. Tomás Rodríguez Bachiller (1899-1980)
    • In particular he attended Emile Borel's course on elasticity, Jules Drach's course on contact transformations, Emile Picard's course on algebraic curves and surfaces, Elie Cartan's course on fluid mechanics, Jacques Hadamard's course on differential equations, the course that Claude Guichard (1861-1924) delivered on differential geometry and Laplace transformations, Henri Lebesgue's course on topology and Ernest Vessiot's courses on partial differential equations and on group theory.

  173. Louis Arbogast (1759-1803)
    • The formal algebraic manipulation of series investigated by Lagrange and Laplace in the 1770s was put in the form of operator equalities by Arbogast in 1800 in Calcul des derivations.

  174. Theodore Strong (1790-1869)
    • The use of Leibniz's approach, as developed by Laplace and Lagrange, was used by Strong in his papers from about 1825 onwards so he participated actively in the introduction of the continental approach to differential and integral calculus into America.

  175. Abraham de Moivre (1667-1754)
    • owes more to [de Moivre] than any other mathematician, with the single exception of Laplace.

  176. Konrad Knopp (1882-1957)
    • After he retired Knopp continued to publish interesting papers such as Zwei Abelsche Satze (1952) in which he proved abelian theorems for Laplace and Abel transforms which are closely related to the well-known Tauberian theorems of Karamata.

  177. Étienne Bobillier (1798-1840)
    • Following the defeat of Napoleon Bonaparte, there was a debate in 1816 whether the Ecole should be closed but, mainly due to efforts by Laplace, it was decided that it should continue to operate but with a smaller intake and some changes to the syllabus, particularly dropping of the course in military arts.

  178. Blagoj Popov (1923-2014)
    • Nowadays, looking back at the list of his publications, it appears that there is no kind of differential equation or special function that has not been studied by him! He had investigated: the equation of ballistics, the hypergeometric, Riccati, Legendre, confluent hypergeometric, Bessel, Weber, Hermite, Darboux, Whittaker, and Laplace differential equations; orthogonal polynomials, Legendre, Gegenbauer, Jacobi, Hermite, Laguerre, Bernoulli, Bessel, and Chebyshev polynomials, the associate spherical Legendre functions, the ultraspherical polynomials, the generalized Legendre and q-Appell polynomials.

  179. Ivan Georgievich Petrovsky (1901-1973)
    • The 1928 paper deals with the Dirichlet problem for Laplace's equation and in the 1929 paper he solved a problem originally posed by Lebesgue.

  180. John Craig (1663-1731)
    • Stigler examines this work in detail in [',' S M Stigler, John Craig and the probability of history : from the death of Christ to the birth of Laplace, Journal of the American Statistical Association 81 (1986), 879-887.','6] claiming that this is an "underappreciated book" containing [',' Biography by Andrew I Dale, in Dictionary of National Biography (Oxford, 2004).','2]:- .

  181. Leonhard Euler (1707-1783)
    • He published a number of major pieces of work through the 1750s setting up the main formulae for the topic, the continuity equation, the Laplace velocity potential equation, and the Euler equations for the motion of an inviscid incompressible fluid.

  182. Sylvestre Lacroix (1765-1843)
    • Laplace had been an examiner at the Royal Artillery Corps since 1784, but before the Reign of Terror he left Paris with his family.

  183. Sophie Germain (1776-1831)
    • Germain attempted to extend her research, in a paper submitted in 1825 to a commission of the Institut de France, whose members included Poisson, Gaspard de Prony and Laplace.

  184. Spiru Haret (1851-1912)
    • "Spiru Haret's theorem" is to be naturally added to the logical succession of theorems with respect to this problem known as "Laplace-Lagrange theorem" and "Poisson's theorem".

  185. Onorato Nicoletti (1872-1929)
    • The other works relate to ordinary differential equations, or to those with partial derivatives also of a higher order than the 2nd, and they all have particular importance for the completion of the results obtained with the method of successive approximations and with that of Riemann as well as for the studies that are taking place on the 2nd order equations of hyperbolic type, in which the Laplace series is finite.

  186. Viktor Yakovlevich Bunyakovskii (1804-1889)
    • Bunyakovskii's book also attempts to make Laplace's Theorie analytique des probabilites (1812) more accessible.

History Topics

  1. Black holes
    • Another mathematical 'proof' was however offered independently of Michell by Pierre-Simon Laplace in 1799 in favour of what Michell had proposed, but with different conclusions on the ratios of density and size.
    • Like Michell, Laplace was working with the assumption that light was formed of particles behaving like projectiles.
    • Moreover, his proof was only provided after the insistence of German astronomer Franz Xaver von Zach (1754-1832), who demanded more than the brief quantitative reasoning that was given in Laplace's original 1796 paper Exposition du Systeme du Monde.
    • There is even some debate as to whether or not Laplace even believed in black holes.
    • Both Laplace and Michell were working with inadequate laws of light.
    • They were also both wrong in their predictions of what stellar black holes were like [',' C Montgomery, W Orchiston and I Whittingham, Michell, Laplace and the origin of the black hole concept, Journal of Astronomical History and Heritage 12 (2) (2009), 90-96.','26]:- .
    • However, like many before, and many after, who worked on the physics behind black holes, Laplace and Hawking included, Einstein doubted the existence of such a physical body being possible, due to the requirement of the physical existence of a singularity.

  2. Matrices and determinants
    • He also knew that a determinant could be expanded using any column - what is now called the Laplace expansion.
      Go directly to this paragraph
    • In 1772 Laplace claimed that the methods introduced by Cramer and Bezout were impractical and, in a paper where he studied the orbits of the inner planets, he discussed the solution of systems of linear equations without actually calculating it, by using determinants.
      Go directly to this paragraph
    • Rather surprisingly Laplace used the word 'resultant' for what we now call the determinant: surprising since it is the same word as used by Leibniz yet Laplace must have been unaware of Leibniz's work.
      Go directly to this paragraph
    • Laplace gave the expansion of a determinant which is now named after him.
      Go directly to this paragraph
    • However this comment is made with hindsight since Lagrange himself saw no connection between his work and that of Laplace and Vandermonde.

  3. Orbits
    • Laplace, from 1774 onwards, became an important contributor to the attempt of the theoreticians to explain the observations of the observers.
      Go directly to this paragraph
    • Lagrange introduced the method of variation of the arbitrary constants in a paper in 1776 stating that the method was of interest in celestial mechanics and, in special cases, had been already been used by Euler, Laplace and himself.
      Go directly to this paragraph
    • Laplace read a memoir to the Academie des Sciences on 23 November 1785 in which he gave a theoretical explanation of all the remaining major discrepancies between theory and observation of all the planets and their moons excluding Uranus.
      Go directly to this paragraph
    • Laplace's work of 1787, that of Adams of 1854 and later Delaunay's work described below eventually provided solutions.
      Go directly to this paragraph
    • The stability proofs of Lagrange and Laplace became inconclusive after this result.
      Go directly to this paragraph

  4. Indian numerals
    • It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics.
    • Laplace wrote:- .
    • The second aspect of the Indian number system which we want to investigate here is the place value system which, as Laplace comments in the quote which we gave at the beginning of this article, seems "so simple that its significance and profound importance is no longer appreciated." We should also note the fact, which is important to both aspects, that the Indian number systems are almost exclusively base 10, as opposed to the Babylonian base 60 systems.
    • All that we know is that the place-value system of the Indians, however it arose, was transmitted to the Arabs and later into Europe to have, in the words of Laplace, profound importance on the development of mathematics.

  5. 20th century time
    • By this he was thinking about Laplace's realisation that Newton's laws completely determined the future if the position, mass and movement of every particle were known.
    • Laplace was, of course, right, but Newton on the other hand had based his theory on absolute space and absolute time and the positions and velocities of the particles were given with respect to this absolute coordinate system.
    • Even in this form it has a direct consequence for aspects of time we have already discussed, for it means that Laplace's realisation that Newton's laws meant that the future was completely determined by the present would not extend to quantum theory.

  6. Fund theorem of algebra
    • Laplace, in 1795, tried to prove the FTA using a completely different approach using the discriminant of a polynomial.
      Go directly to this paragraph
    • Gauss's criticisms of the Lagrange-Laplace proofs did not seem to find immediate favour in France.
      Go directly to this paragraph
    • Even the 1828 Edition, edited by Poinsot, still expresses complete satisfaction with the Lagrange-Laplace proofs and no mention of the Gauss criticisms.
      Go directly to this paragraph

  7. Decimal time
    • Laplace was enthusiastic and had his watch converted to the new time.
    • However Laplace was one of the few to greet the changes in the units of time and angle with any enthusiasm.
    • Laplace, now a senator, stated that the new calendar had scientific flaws and should be scrapped.

  8. Measurement
    • Indeed, probably Laplace and others were more interested in finding the shape of the Earth rather than the length of the metre.
    • However between these dates the French Revolution progressed to the stage where the Academie des Sciences was abolished in August 1793 but before that Borda, Lagrange and Laplace had computed a provisional value for the metre based on the survey carried out by Cassini de Thury in 1740.

  9. African women 1
    • She has published around 15 papers including A characteristic property of the generalized hyperexponential distribution (1993), On the exponentiated Weibull distribution (2003), A note on some characterizations of the hyperexponential distribution (2005), On Bayesian sample size determination (2011) and The Kumaraswamy-Laplace distribution (2016).
    • The resulting formulation together with the Laplace transform technique is applied to a variety problems.

  10. Classical time
    • There was another interesting consequence of Newton's description of the universe based on his precise mathematical laws, and this was fully understood by Laplace.
    • Laplace correctly argued that given the laws of mechanics, the complete picture of the past and future world is encapsulated in the present world.

  11. General relativity

  12. African women I
    • She has published around 15 papers including A characteristic property of the generalized hyperexponential distribution (1993), On the exponentiated Weibull distribution (2003), A note on some characterizations of the hyperexponential distribution (2005), On Bayesian sample size determination (2011) and The Kumaraswamy-Laplace distribution (2016).

  13. History overview
    • The period around the turn of the century saw Laplace's great work on celestial mechanics as well as major progress in synthetic geometry by Monge and Carnot.
      Go directly to this paragraph

  14. References for Black holes
    • C Montgomery, W Orchiston and I Whittingham, Michell, Laplace and the origin of the black hole concept, Journal of Astronomical History and Heritage 12 (2) (2009), 90-96.

  15. Indian mathematics
    • Laplace put this with great clarity:- .

  16. Classical light
    • Fresnel wrote a paper giving the mathematical basis for his wave theory of light and in 1819 the committee, with Arago as chairman, and including Poisson, Biot and Laplace met to consider his work.

  17. Weather forecasting
    • Spherical harmonics Ynm(λ, φ) are the angular part of the solution to Laplace's equation.

Societies etc

  1. Turin Mathematical Society
    • The same volume contains Recherches sur le calcul integral aux differences infiniment petites, et aux differences finies by Laplace showing that the journal had already gained a high reputation.
    • This paper contained equations which Laplace stated were important in mechanics and physical astronomy.

  2. Fellows of the RSE
    • Pierre Simon Laplace1813More infoMacTutor biography .

  3. Fellows of the RSE
    • Pierre Simon Laplace1813More infoMacTutor biography .


  1. Rue Laplace
    • Rue Laplace .

  2. Laplace
    • Pierre Simon Laplace .

  3. AMS Steele Prize
    • He later extended this work to a spectral theory for the automorphic Laplace operator, relying on the Radon transform on horospheres to avoid Eisenstein series.

  4. Fellow of the Royal Society
    • Pierre S Laplace 1789 .

  5. Lunar features
    • (W) (L) Promontorium Laplace .

  6. Eiffel Tower
    • Laplace .

  7. Fellows of the RSE
    • Pierre Simon Laplace1813More infoMacTutor biography .

  8. Fellows of the RSE
    • Pierre Simon Laplace1813More infoMacTutor biography .

  9. Eiffel scientists
    • Laplace (Astronomer and Mathematician) .

  10. International Congress Speaker
    • Salomon Bochner, Laplace Operator on Manifolds.

  11. Lunar features
    • Promontorium Laplace .

  12. Paris street names
    • Rue Laplace ( 5th Arrondissement) WnMn .

  13. Lectures to the Mathematical Society of Vienna
    • Lucius Hanni: Die Verwendung des Laplace-Abelschen Integrals in der neueren Funktionentheorie.


  1. References for Pierre-Simon Laplace
    • References for Pierre-Simon Laplace .
    • .
    • H Bernhard, Laplace, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).
    • C C Gillispie, Pierre-Simon Laplace.
    • B A Vorontsov-Vel'yaminov, Laplace (Russian), 'Nauka' (Moscow, 1985).
    • V Banfi, The origin of the solar system according to P S Laplace (Italian), Atti Accad.
    • F Barone, The epistemology of Pierre-Simon de Laplace (Italian), Atti Accad.
    • L Brandt, Uber das Bahnbestimmungsproblem bei Gauss und Laplace.
    • P Brosche, Laplace schreibt nach Gotha, Ber.
    • B Bru, L'a-peu-pres et l'a-fort-peu-pres au temps de Laplace, in L'a-peu-pres (Paris, 1988), 87-103.
    • W G Cochran, Laplace's ratio estimator, in Contributions to survey sampling and applied statistics (New York, 1978), 3-10.
    • A I Dale, Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem, Arch.
    • M A B Deakin, The ascendancy of the Laplace transform and how it came about, Arch.
    • M A B Deakin, Corrigendum: 'Operational calculus and the Laplace transform', Austral.
    • M A B Deakin, Euler's version of the Laplace transform, Amer.
    • M A B Deakin, Operational calculus and the Laplace transform, Austral.
    • M A B Deakin, The development of the Laplace transform, 1737-1937 I : Euler to Spitzer, 1737-1880, Arch.
    • M A B Deakin, The true origins of the Laplace transform, Math.
    • J Dhombres, La theorie de la capillarite selon Laplace : mathematisation superficielle ou etendue?, La mathematisation 1780-1830, Rev.
    • Les lecons de Laplace a l'Ecole Normale de l'an III, Rev.
    • P Dupont, Laplace and the indifference principle in the 'Essai philosophique des probabilites' (Italian), Rend.
    • J Fourier, Eloge historique de M le Marquis de Laplace, MASIF 10 (1831).
    • E Frankel, The search for a corpuscular theory of double refraction : Malus, Laplace and the prize competition of 1808, Centaurus 18 (1973/74), 223-245.
    • H H Frisinger, Mathematicians in the history of meteorology: the pressure-height problem from Pascal to Laplace, Historia Math.
    • extensional probabilities from their origins to Laplace, Historia Math.
    • C C Gillispie, Memoires inedits ou anonymes de Laplace sur la theorie des erreurs, les polynomes de Legendre, et la philosophie des probabilites, Rev.
    • S Gindikin, Pierre-Simon Laplace (Russian), Kvant (12) (1977), 12-21.
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    • B V Gnedenko, Pierre Simon Laplace (1749-1827) on the 150th anniversary of his death (Bulgarian), Fiz.-Mat.
    • I A Golovinskii, How was the Laplace transform introduced? (Russian), Istor.-Mat.
    • I A Golovinskii, Laplace interpolation series (Russian), Istor.-Mat.
    • I A Golovinskii, The importance of the discovery of the Laplace transform to the development of interpolation methods (Russian), Voprosy Istor.
    • M A Gomez Villegas, The problem of inverse probability : Bayes and Laplace (Spanish), in Current perspectives in logic and philosophy of science (Spanish) (Madrid, 1994), 385-396.
    • I Grattan-Guinness, Before Bowditch : Henry Harte's translation of Books 1 and 2 of Laplace's Mecanique celeste, NTM Schr.
    • I Grattan-Guinness, Thus it mysteriously appears : impressions of Laplace's use of series, Rechnen mit dem Unendlichen (Basel, 1990), 95-102.
    • J Hadamard, Celebration du deuxieme centenaire de la naissance de P S Laplace, Arch.
    • A M Hinz, Laplace in Calvados, Math.
    • M Jacobsen, Laplace and the origin of the Ornstein-Uhlenbeck process, Bernoulli 2 (3) (1996), 271-286.
    • S L Jaki, The five forms of Laplace's cosmogony, Amer.
    • J Langins, Sur l'enseignement et les examens a l'Ecole polytechnique sous le Directoire: a propos d'une lettre inedite de Laplace, Rev.
    • B Ju Levin, On the history of the term 'Kant-Laplace hypothesis' (Russian), Voprosy Istor.
    • B Yu Levin, Laplace's cosmogonic hypothesis (history of its creation and publication) (Russian), Voprosy Istor.
    • W Lorey, Die Bedeutung von Pierre Simon Laplace (28.3.
    • J Merleau-Ponty, Situation et role de l'hypothese cosmogonique dans la pensee cosmologique de Laplace, Rev.
    • J Merleau-Ponty, Erratum: 'Situation et role de l'hypothese cosmogonique dans la pensee cosmologique de Laplace', Rev.
    • V V Pavlovskaja, The problem of the stability of the equilibrium of a revolving fluid in the works of d'Alembert and Laplace (Russian), in Problems in the history of mathematics and mechanics (Kiev, 1977), 58-67.
    • J-B Pecot, Le probleme de l'ellipsoide et l'analyse harmonique : la controverse entre Legendre et Laplace, in Analyse diophantienne et geometrie algebrique (Paris, 1993), 113-157.
    • S S Petrova, On the history of Laplace's method of cascades (Russian), in Studies in the history of mathematics 19 'Nauka' (Moscow, 1974), 125-131, 301.
    • S S Petrova, Early history of the Laplace transform (Russian), Istor.-Mat.
    • Newton and Laplace-their life and work (Bulgarian), Fiz.-Mat.
    • R L Plackett, The influence of Laplace and Gauss in Britain, Bull.
    • A W Richeson, Laplace's contribution to pure mathematics, Nat.
    • L M R Saraiva, Laplace, Lavoisier and the quantification of heat, Physis Riv.
    • I Schneider, Laplace and thereafter : the status of probability calculus in the nineteenth century, in The probabilistic revolution 1 (Cambridge, MA-London, 1987), 191-214.
    • F Sebastiani, The microscopic-caloric theories of gases of Laplace, Ampere, Poisson and Prevost (Italian), Physis - Riv.
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.
    • O B Sheynin, The probability theory of P-S Laplace (Russian), Istor.-Mat.
    • O B Sheynin, P S Laplace's work on probability, Arch.
    • O B Sheynin, On the history of the de Moivre-Laplace limit theorems (Russian), in History and methodology of natural sciences No.
    • O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat.
    • V S Sologub, On the first integration methods of the Laplace equation (Ukrainian), Istor.-Mat.
    • S M Stigler, Laplace's 1774 memoir on inverse probability, Statist.
    • S M Stigler, Studies in the history of probability and statistics XXXIV: Napoleonic statistics : the work of Laplace, Biometrika 62 (2) (1975), 503-517.
    • S M Stigler, Laplace's early work : chronology and citations, Isis 69 (247) (1978), 234-254.
    • S M Stigler, Studies in the history of probability and statistics XXXII : Laplace, Fisher, and the discovery of the concept of sufficiency, Biometrika 60 (1973), 439-445.
    • D van Dantzig, Laplace, probabiliste et statisticien, et ses precurseurs, Arch.
    • E T Whittaker, Works of Laplace, Mathematical Gazette 33 (1949), 1-12.
    • E T Whittaker, Laplace, Amer.
    • C Wilson, The great inequality of Jupiter and Saturn : from Kepler to Laplace, Arch.
    • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.

  2. References for Michel Plancherel
    • Sur l'application aux series de Laplace du procede de sommation de M.
    • Sur la sommation des series de Laplace de de Legendre.
    • Sur le role de la transformation de Laplace dans l'integration d'une classe de problemes mixtes du type hyperbolique et sur les developpements en series d'un couple de fonctions arbitraires.

  3. References for Adrien-Marie Legendre
    • C C Gillispie, Memoires inedits ou anonymes de Laplace sur la theorie des erreurs, les polynomes de Legendre, et la philosophie des probabilites, Rev.
    • J-B Pecot, Le probleme de l'ellipsoide et l'analyse harmonique : la controverse entre Legendre et Laplace, in Analyse diophantienne et geometrie algebrique (Paris, 1993), 113-157.

  4. References for Émile Clapeyron
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.

  5. References for Sadi Carnot
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis-Riv.

  6. References for Rudolf Clausius
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.

  7. References for Gaspard Monge
    • J J Bikerman, Capillarity before Laplace : Clairaut, Segner, Monge, Young, Arch.

  8. References for Abraham de Moivre
    • O B Sheynin, On the history of the de Moivre-Laplace limit theorems (Russian), in History and methodology of natural sciences IX : Mechanics, mathematics (Moscow, 1970), 199-211.

  9. References for André-Marie Ampère
    • F Sebastiani, The microscopic-caloric theories of gases of Laplace, Ampere, Poisson and Prevost (Italian), Physis - Riv.

  10. References for John Craig
    • S M Stigler, John Craig and the probability of history : from the death of Christ to the birth of Laplace, Journal of the American Statistical Association 81 (1986), 879-887.

  11. References for Sylvestre Lacroix
    • R Taton, Laplace et Sylvestre Francois Lacroix, in Rev.

  12. References for Johann Heinrich Lambert
    • U Garibaldi and M A Penco, Probability theory and physics between Bernoulli and Laplace : the contribution of J H Lambert (1728-1777) (Italian), in Proceedings of the fifth national congress on the history of physics, Rome, 1984, Rend.

  13. References for Blaise Pascal
    • H H Frisinger, Mathematicians in the history of meteorology : the pressure-height problem from Pascal to Laplace, Historia Math.

  14. References for Henri Andoyer
    • F Cajori, Review: L'Oeuvre scientifique de Laplace, by Henri Andoyer, Bull.

  15. References for Josif Zakharovich Shtokalo
    • K G Valeev, The development of I Z Shtokalo's ideas on the application of the Laplace transform (Russian), Differencial'nye Uravnenija 13 (11) (1977), 1926-1931; 2106.

  16. References for Georges Buffon
    • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.

  17. References for Joseph Bertrand
    • The Laplace integral and the Bertrand problem (Russian), Investigations in the history of mechanics ('Nauka', Moscow, 1981), 128-140; 311.

  18. References for Henri Poincaré
    • M A B Deakin, The development of the Laplace transform, 1737-1937.

  19. References for Johann Segner
    • J J Bikerman, Capillarity before Laplace : Clairaut, Segner, Monge, Young, Arch.

  20. References for Giovanni Plana
    • G Tagliaferri and P Tucci, Carlini and Plana on the theory of the moon and their dispute with Laplace, Ann.

  21. References for Étienne Louis Malus
    • E Frankel, The search for a corpuscular theory of double refraction : Malus, Laplace and the prize competition of 1808, Centaurus 18 (1973/74), 223-245.

  22. References for Thomas Bayes
    • A I Dale, Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem, Arch.

  23. References for Carl Friedrich Gauss
    • R L Plackett, The influence of Laplace and Gauss in Britain, Bull.

  24. References for Richard Price
    • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.

  25. References for Jean d'Alembert
    • V V Pavlovskaja, The problem of the stability of the equilibrium of a revolving fluid in the works of d'Alembert and Laplace (Russian), in Problems in the history of mathematics and mechanics (Kiev, 1977), 58-67.

Additional material

  1. Babbage Laplace Fourier Biot
    • Charles Babbage on Laplace, Fourier and Biot .
    • In Passages from the Life of a Philosopher (Longman, Green, Longman, Roberts, & Green, London, 1864), Charles Babbage relates meetings with Pierre-Simon Laplace, Joseph Fourier and Jean-Baptiste Biot: .
    • One morning John Herschel and I called on Laplace who spoke to us of various English works on mathematical subjects.
    • The volume of the "Memoirs of the Analytical Society" though really our joint production, was not known to be such, and it was also clear that Laplace did not refer to that work.
    • Perceiving that we did not recognise the name of the author to whom he referred, Laplace varied the pronunciation by calling him vous deux; the first word being pronounced as the French word "vous" and the second as the English word "deuce." Upon further explanation, it turned out that Laplace meant to speak of a work published by Woodhouse, whose name is in the pronunciation of the French so very like vous deux.
    • .

  2. Laplace: 'Méchanique Céleste
    • Laplace: Mechanique Celeste .
    • Pierre-Simon Laplace published the first two volumes of Mechanique Celeste in 1799.
    • Nathaniel Bowditch translated Laplace's book into English and this English translation was published in 1829.
    • Below we give Bowditch's translation of Laplace's Preface:- .
    • .

  3. Laplace on 'new stars
    • Laplace on "new stars" .
    • Variable stars had been known for 200 years when Laplace wrote Exposition du systeme du monde (1796).
    • Laplace wrote about supernovae in Exposition du systeme du monde in 1796:- .
    • .

  4. Laplace: 'Essay on probabilities
    • Laplace: Essay on probabilities .
    • Laplace wrote A philosophical essay on probabilities which was translated by F W Truscott and F L Emory and was published by Dover in 1953.
    • .

  5. George William Hill's new theory of Jupiter and Saturn
    • But these terms not bringing about a reconciliation between observation and theory, Lagrange and Laplace were led to make their notable researches on the possibility of secular equations in the mean motions of the planets.
    • At length the whole difficulty with Jupiter and Saturn was removed by Laplace's discovery of the great inequalities in 1786.
    • This great success seems to have stirred up Laplace and his collaborators to pushing the approximations still further.
    • The results he obtained failed to satisfy an equation of condition which Laplace had employed in his investigation.
    • After some discussion Laplace abandoned his equation and substituted for it another, which Plana's results were as far from satisfying as before.
    • Pontecoulant then, taking up the subject, discovered that Laplace's results had been taken with the wrong sign, and that Plana had made errors of some importance in his investigation.
    • Neither Laplace's, Plana's, nor Pontecoulant's determination of these second-order terms can be regarded as anything else than a very rude and inadequate approximation.
    • In the Mecanique Celeste, Laplace had determined all long-period inequalities as if they were to be applied to the mean longitude, and had so directed they should, while the short-period ones were derived as if they were to be added to the true longitude.
    • For Laplace has nowhere shown how these two modes of application can be employed in unison.

  6. Bompiani publications
    • Enrico Bompiani, Sull'equazione di Laplace, Rend.
    • Enrico Bompiani, Sur les configurations de Laplace, Comptes Rendus de l'Ac.
    • Enrico Bompiani, Pour la geometrie de l'equation de Laplace, Comptes Rendus de l'Ac.
    • Enrico Bompiani, Risoluzione geometrica del problema di Moutard sulla costruzione delle equazioni di Laplace ad integrale esplicito, Rend.
    • Enrico Bompiani, Sur les equations de Laplace a invariants egaux, Comptes Rendus de l'Ac.
    • Enrico Bompiani, Ricerche analitiche e geometriche sull'equazione di Laplace, Rend.
    • Enrico Bompiani, Sulla geometria dell'equazione di Laplace, Rend.
    • Enrico Bompiani, Postilla sull'equazione di Laplace, Boll.
    • Enrico Bompiani, Un invariante integrale dell'equazione di Laplace, Boll.

  7. Hille publications
    • (With J D Tamarkin) On the theory of Laplace integrals, Proc.
    • (With J D Tamarkin) On the theory of Laplace integrals.
    • On Laplace integrals, Att.
    • Bilinear formulas in the theory of the transformation of Laplace, Composit.
    • (With W B Caton) Laguerre polynomials and Laplace integrals, Duke Math.
    • Review: Handbuch der Laplace-Transformation.
    • Theorie der Laplace- Transformation, by G Doetsch, Bull.
    • Some extremal properties of Laplace transforms, Math.

  8. Rios publications
    • Sixto Rios Garcia, La hiperconvergencia en las integrales de Laplace-Stieltjes, Boletin del Seminario Matematico Argentino 4 (17) (1935), 47-50.
    • Sixto Rios Garcia, Un teorema sobre las singularidades de las integrales de Laplace-Stieltjes, Bol.
    • Sixto Rios Garcia, Un teorema sobre las singularidades de las integrales de Laplace-Stieltjes, Revista Matematica Hispano-Americana 11 (1936), 26-29.
    • Sixto Rios Garcia, On the singularities of the Laplace integral (Spanish), Portugaliae Math.
    • Sixto Rios Garcia, On the singularities of the Laplace integral (Spanish), Revista Acad.
    • Sixto Rios Garcia, Some probability laws and stochastic processes which reduce to a general Laplace-Stieltjes type (Spanish), Trabajos Estadistica 4 (1953), 3-10.
    • Sixto Rios Garcia, Some probability laws and stochastic processes which reduce to a general type of Laplace-Stieltjes (Spanish), Revista Mat.
    • Sixto Rios Garcia, Some probability laws and stochastic processes deduced from a Laplace-Stieltjes integral (Spanish), Revista Acad.

  9. O'Brien tracts
    • The subjects treated of in the following Tracts are, Laplace's Coefficients; the Investigation of the Figure of the Earth on the Hypothesis of its Original Fluidity; the Equations of Motion of a Rigid Body about its Centre of Gravity; and the Application of these Equations to the case of the Earth.
    • The Author has put both these subjects together, commencing with the Figure of the Earth, and introducing Laplace's Coefficients when occasion required the; this being perhaps the best and simplest way of exhibiting the nature and use of these coefficients.
    • The Author has deduced the equations of motion of a rigid body about its centre of gravity by a method which he hopes will be found, less objectionable than that in which the composition and resolution of angular velocities are employed, and less complex than that given by Laplace and Poisson ; he has also endeavoured to simplify the application of these equations to the case of the Earth.
    • In the Second Part, which will shortly be published, he intends, among other things, to give some account of the controversies which Laplace's Coefficients have given rise to; to investigate more fully the nature and properties of these functions; to give instances of their use in various problems; for this purpose to explain the mathematical theory of Electricity; to consider more particularly the Equations of motion of a rigid body about its centre of gravity, and the conclusions that may be drawn from them; to give the theory of Jupiter's Satellites, and of Librations of the Moon; and to say something on the subject of Tides.

  10. Rios's books
    • This publication gives an account of some of the properties of Dirichlet series in the complex domain and their extension to Laplace-Stieltjes integrals.
    • It antedates the recent publications of Mandelbrojt, and apparently Widder's book [The Laplace Transform, 1941] was not available to the author, so that some recent results are not included.
    • These include a discussion of the class of all Laplace-Stieltjes transforms as a complete metric space, the distance between two elements being eCif the abscissa of convergence of their difference is C, elements at zero distance being identified.
    • In these lectures (written in collaboration with L Vigil) the author covers a wide variety of topics in the representation of analytic functions of a complex variable: Runge's theorems; analytic continuation by overconvergence and by rearrangement (he constructs, among other examples, a "universal" series of polynomials which can be rearranged to converge uniformly to any prescribed analytic function in any desired region); Mittag-Leffler, Borel and Painleve expansions; analytic continuation by summation of series; representation of functions by Laplace integrals and by Dirichlet, factorial, interpolation and Lambert series.

  11. Horace Lamb addresses the British Association in 1904
    • When he came to manhood Lagrange, Laplace, Poisson, Fourier, Fresnel, Ampere, had but lately passed away.
    • When the foundations of Analytical Dynamics had been laid by Euler and d'Alembert, the first important application was naturally to the problems of Gravitational Astronomy; this formed, of course, the chief work of Laplace, Lagrange, and others.
    • It has suggested many important analytical results, and still gives the best and simplest intuitive foundation for a whole class of theorems which are otherwise hard to comprehend in their various relations, such as Fourier's theorem, Laplace's expansion, Bessel's functions, and the like.

  12. Joseph Fourier on his teachers
    • Among his teachers were Laplace, Monge, and Lagrange, and Fourier gave charming descriptions of these famous mathematicians.
    • Laplace was 45 years old when Fourier attended his lectures:- .
    • Laplace seems quite young; his voice is quiet but clear, and he speaks precisely, though not very fluently; his appearance is pleasant, and he dresses very simply; he is of medium height.

  13. Herivel's books
    • If Fourier can indeed be classified as a physicist - and I feel he more appropriately belongs with the applied mathematicians like Laplace, Poisson, and Cauchy than with physicists such as Fresnel and Ampere-some discussion of the important developments in early 19th-century French physics would seem appropriate.
    • Now recognized as a masterpiece of mathematical analysis and theoretical physics, it was not highly admired by the leading mathematicians at the Academy of Sciences, Laplace, Lagrange, Poisson, and Biot.
    • The documents include eight letters of Fourier, and ten manuscripts by Fourier, Laplace, Biot, and Poisson that help to clarify the contents of the letters.

  14. R A Fisher: 'History of Statistics
    • Whereas Bayes excelled in logical penetration, Laplace (1820) was unrivalled for his mastery of analytic technique.
    • These seem to have been later discovered independently by Thiele (1889), but mathematically Laplace's methods were more powerful than Thiele's and far more influential on the development of the subject in France and England.
    • A direct result of Laplace's study of the distribution of the resultant of numerous independent causes was the recognition of the normal law of error, a law more usually ascribed, with some reason, to his great contemporary, Gauss.

  15. Graves's papers
    • (date of paper 1855) (with Robert Carmichael) On Laplace's Equation and the Calculus of Quaternions, Proceedings of the Royal Irish Academy (1836-1869) 6 (1853-1857), 216-223.
    • (date of paper 1855) On the Solution of the Equation of Laplace's Functions, Proceedings of the Royal Irish Academy (1836-1869) 6 (1853-1857), 162-171.
    • (date of paper 1855) On the Solution of the Equation of Laplace's Functions (Continued), Proceedings of the Royal Irish Academy (1836-1869) 6 (1853-1857), 186-194.

  16. Andrew Forsyth addresses the British Association in 1905, Part 2
    • The beginnings were made by the Bernoullis (a family that must be of supreme interest to Dr Francis Galton in his latest statistical compilations, for it contained no fewer than seven mathematicians of mark, distributed over three generations), but the main achievements are due to Euler, Lagrange, and Laplace.
    • It was made, in the main, by Lagrange, as regards the wider theory, and by Laplace, as regards the amplitude of detailed application.
    • In that year Laplace published the last progressive instalment of his great treatise on Celestial Mechanics, the portion that still remained for the future being solely of an historical character; the great number of astronomical phenomena which he had been able to explain by his mathematical presentation of the consequences of the Newtonian theory would, by themselves, have been sufficient to give confidence in the validity of that theory.

  17. Santalo honorary doctorate
    • Laplace (1749-1827) in his Analytical Theory of Probabilities (1812), considers the plane divided into congruent rectangles by two series of parallel lines and calculates the probability that a needle thrown at random on the plane does not cut any of those straight lines (problem of the Laplace needle).
    • The problems of Buffon or Laplace needle motivate the problem of measuring sets of lines in the plane.

  18. Smith Autograph Papers
    • (20) Babbage Visits Mme Laplace.
    • Alexis Bouvard (1767-1843) took him to see the widow of Laplace.
    • At twelve he was contesting with Zerah Colburn, the American "calculating boy," and at sixteen he was reading Laplace's Mecanique Celeste and pointing out an error in the work of the great French master.

  19. Sansone books
    • The Laplace integral.
    • Among the topics discussed are: power series, elementary functions, Cauchy integral theorem, residue theory, Weierstrass factor theorem, Mittag-Leffler theorem, elliptic functions, integral functions of finite order, Dirichlet series, Riemann zeta function, Laplace integral and asymptotic series.
    • the technique of Lyapunov functions and a technique due to Popov which is based on Laplace transform methods.

  20. L R Ford - Differential Equations
    • Subsequent chapters cover special methods for equations of first order, linear equations of any order with a brief account of the use of the Laplace transform, solution in series of the hypergeometric, Legendre's and Bessel's equations, approximate numerical solutions, and two chapters on partial differential equations.
    • General solutions of simple types of partial differential equations are obtained before separation of variables is used to solve problems of vibration and the Laplace equation in two dimensions.

  21. Walk Around Paris
    • They include Lagrange, Laplace, Cauchy, Poisson, Monge, and many others.
    • He was friends with Berthollet, Lagrange and Laplace.

  22. More Smith History books
    • Portraits of the following men make up Portfolio Number Two: Euclid, Cardan, Kepler, Fermat, Pascal, Euler, Laplace, Cauchy, Jacobi, Hamilton, Cayley, Chebyshev, Poincare.
    • "Laplace lived in a period of one of the world's greatest wars - the French Revolution.

  23. Kelvin on the sun, Part 2
    • This is just the beginning postulated by Laplace for his nebular theory of the evolution of the solar system which, founded on the natural history of the stellar universe, as observed by the elder Herschel, and completed in details by the profound dynamical judgment and imaginative genius of Laplace, seems converted by thermodynamics into a necessary truth, if we make no other uncertain assumption than that the materials at present constituting the dead matter of the solar system have existed under the laws of dead matter for a hundred million years.

  24. Franklin's textbooks
    • There is a section on the Laplace transformation, one on Poisson's sum formula, and a brief exposition of the theory of partial differential equations of the first order.
    • It is designed to show them how to operate with complex quantities and how to solve problems for their solution on the use of Fourier series and integrals, and Laplace transforms.

  25. Douglas Jones's books
    • The study of more advanced topics such as partial differential equations, Laplace transforms and ultra-distributions should also make it a valuable source for researchers.
    • Asymptotics is an old topic in applied analysis, dating back to the time of Laplace.

  26. Segel books
    • Chapter 3: Random Processes and Partial Differential Equations; Random walk in one dimension; Langevin's equation; Asymptotic series, Laplace's method, gamma function, Stirling's formula; A difference equation and its limit; Further considerations pertinent to the relationship between probability and partial differential equations; .
    • Chapter 16: Potential Theory; Equations of Laplace and Poisson; Green's functions; Diffraction of acoustic waves by a hole.

  27. Somerville's Booklist

  28. Murray books
    • In the first there is a discussion of concepts and definitions of asymptotic expansions, sequences and series, and in the second Watson's lemma and Laplace's method for integrals are considered.
    • Readers should be familiar with (or prepared to read up about) the phase plane, matrix methods for linear ordinary differential equations, asymptotic methods, elasticity theory, Laplace transforms, and so on.

  29. Puig Adam publications
    • Pedro Puig Adam, La transformacion de Laplace en el tratamiento matematico de fenomenos fisicos, Revista Matematica Hispano-Americana (1951).
    • Pedro Puig Adam, Transformee de Laplace des fonctions empiriquement donnees, Actas del Coloquio Les machines a calculer et la pensee humaine (1951).

  30. Thomas Muir: 'History of determinants
    • 2, which occurs under Laplace, is meant to show that the theorem was not then heard of for the first time, but that Laplace contributed something additional to our knowledge of it.

  31. H S Ruse papers
    • General solutions of Laplace's equation in a simply harmonic manifold (1963).
    • T J Willmore writes: Explicit formulae are obtained for general solutions of Laplace's equation in a real n-cell equipped with a simply harmonic riemannian metric.

  32. Ahrens book of quotes
    • Even Laplace's Cosmological Hypotheses fall in this class.
    • Think only of the masters Laplace and Lagrange! What is more, there has never been a lack of effort to ascertain that the fundamental principles of Mechanics are given a priori, following the example of the axioms of geometry.

  33. Sansone publications
    • Giovanni Sansone, Sulla sommabilita di Cesaro delle serie di Laplace, Atti Accad.
    • Giovanni Sansone, Sulla sommabilita di Cesaro delle serie di Laplace, Atti primo Congr.

  34. Murphy books
    • As an acquaintance with the properties of the remarkable functions treated by Laplace in the Mecanique Celeste Book III is indispensable in investigations respecting electricity, instead of referring to that work I have here introduced them under the form of Preliminary Propositions; I have however followed a different route, making the functions which shall possess those properties, the objects of investigation; and have thus arrived at a more general class of functions (which are of great use in investigations relative to Latent Electricity) and also obtained several new and remarkable theorems with respect to Laplace's functions: it must be added that on referring to Crelle's Journal, I found that M Jacobi had anticipated me with a respect to few of the theorems alluded to.

  35. Samarskii's books
    • The treatment here is classical, with an initial chapter on the classification of second order equations, followed by three chapters on hyperbolic, parabolic and elliptic equations, illustrated by detailed treatments of the wave, heat and Laplace equations.

  36. Whittaker RSE Prize
    • An early and brilliant example was his general solution of Laplace's equation, which might be considered the fundamental partial differential equation of the older physics.

  37. Cotlar publications
    • Mischa Cotlar and Juan Carlos Vignaux, Integrales asimptoticas de Laplace-Stieltjes, Univ.

  38. Rios Honorary Degree
    • ., the historical point of departure is Laplace's rediscovery of Bayes' theorem, which has allowed the construction of inductive logic and decision theory, in competition with each other on more or less convergent paths, always hoping for a general consensus.

  39. Publications of Albert Wangerin
    • Laplace, Ivory, Gauss, Chasles und Dirichlet: Uber die Anziehung homogener Ellipsoide (W Engelmann, Leipzig, 1890).

  40. Alasia publications
    • C Alasia, L'equazione di Laplace, Riv.

  41. William Herschel discoveries
    • Pierre-Simon Laplace independently obtained a similar result from his calculation of the orbit.

  42. H M Macdonald addresses the British Association in 1934
    • The modification necessary in this result to make it applicable to the case of crystalline media was effected by Laplace, who made use of the corpuscular theory of light in his investigation and assumed that the velocity of the light particles in a crystalline medium depended on the direction.

  43. Ernest Hobson addresses the British Association in 1910
    • In the classical period of the eighteenth century, the time of Lagrange and Laplace, the nature of the physical investigations, consisting largely of the detailed working out of problems of gravitational Astronomy in accordance with Newton's law, was such that the passage was easy from the concrete problems to the corresponding abstract mathematical ones.

  44. System Reliability Theory
    • Mathematical tools like matrix algebra, Laplace transform, and limiting arguments are used throughout.

  45. Feller Reviews 3
    • Thus, Chapter III on fluctuations in coin tossing has been completely rewritten; the treatment of the De Moivre-Laplace limit theorem, Chapter VII, has been revised; and the material on branching processes has been expanded.

  46. Milnor's books
    • Milnor's excellent, clear, and laconic style makes the book a real treat ("Eigenvalues of the Laplace operator on certain manifolds", 1964, is less than a page long; the paper contains the first example of isospectral but not isometric compact Riemannian manifolds).

  47. Lectures Vienna Math Soc.html
    • Lucius Hanni: Die Verwendung des Laplace-Abelschen Integrals in der neueren Funktionentheorie.

  48. Centenary of John Leslie
    • He met Humboldt, Laplace, and other famous men.

  49. Zhukovsky (or Jowkowski) aerofoils
    • One of the curious and useful facts about differentiable complex functions is that their real and imaginary parts satisfy Laplace's Equation (a partial differential equation important in many applications from Electricity to Hydrodynamics).

  50. Viola on Amaldi
    • Graduating in 1898 with a thesis on the Laplace transformation, in the same year he attained the ability to teach mathematics in secondary schools.

  51. John Walsh's delusions
    • Laplace's demonstration of the parallelogram of forces is a begging of the question; and the attempts of them all to show that the difference of twenty minutes between the sidereal and actual revolution of the earth round the sun arises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfect quackery.

  52. Charles Tweedie on James Stirling
    • Witness, for example, the tribute of praise rendered by Laplace in his papers on Probability and on the Laws of Functions of very large numbers.

  53. Speiser books
    • The poverty of Hegel's own contribution to the foundations of mathematics was due, Speiser considers, to the lack of interest in mathematics in Germany at the time; France's Lagrange, Laplace, Legendre, Carnot, Dupin, Lame, Monge, Poncelet, Lacroix and Cauchy were challenged in Germany only (but outstandingly) by Gauss.

  54. Brinkley Copley Medal
    • The volume for 1807 contains an important paper, on the General Term of a Series in the Inverse Method of finite Differences; in which, taking up a subject of investigation on which both Lagrange and Laplace had written, he has surmounted a difficulty which had remained even after the investigations of these illustrious geometers.

  55. Sergescu works
    • Le bicentenaire de la naissance de Laplace (1949).

  56. Mannheim publications
    • A Mannheim, Lettre concernant la collection de Memoires de Lagrange, de Monge, de Laplace, etc., transmise par M Biot a M Edmond Bour, Comptes Rendus des Seances de l'Academie des Sciences 62 (1866), 838-839 .

  57. James Clerk Maxwell on the nature of Saturn's rings
    • We know, since it has been demonstrated by Laplace, that a uniform solid ring cannot revolve permanently about a planet.

  58. Montmort's Treize
    • For example Leonhard Euler in Calcul de la probabilite dans le jeu de rencontre (1743), Abraham de Moivre in The Doctrine of Chances (1756), Johann Lambert in Examen d'une espece de superstition ramenee au calcul des probabilites (1773), Edward Waring in An Essay on the Principles of Human Knowledge (1794), and Pierre-Simon Laplace in Theorie Analytique des Probabilites (1812).

  59. Vivanti publications
    • Giulio Vivanti, Sulla trasformazione di Laplace, Palermo Rend.

  60. George Temple's Inaugural Lecture II
    • All our masters, from Laplace to Cauchy, have proceeded in the same way.

  61. Feller Reviews 4
    • Volume II goes very much deeper into the subjects of probability, probability distribution theory of stochastic processes, basic limit theorems, infinitely divisible distributions, Markov processes, renewal theory, random walks, Laplace transforms, characteristic functions, Fourier analysis methods and harmonic analysis.

  62. Basset hydrodynamics
    • The discovery of the general equations of motion was followed up by the investigations of the great French mathematicians Laplace, Lagrange and Poisson, the first of whom has left us a splendid memorial of his genius in his celebrated Theory of the Tides.

  63. Moran reviews
    • Provided they are not intimidated by some of the names - such as Riemann-Stieltjes, Laplace- Stieltjes, Bachelier-Wiener - appearing in Chapter 1, they will find the mathematics in the rest of the book well under control, and serving its proper purpose of clarifying the argument.

  64. Gyula König Prize
    • In this area, where the first classical results are linked with the names of Laplace and Darboux, Szego not only obtains very general results, far overshadowing anything known previously, but he obtains these results exactly because he examines these questions, considered very difficult, using a simple, one can say elementary, method.

  65. Borali-Forti publications
    • C Burali-Forti, Sull'operatore di Laplace per le omografie vettoriali, Atti dell'Accademia dei Lincei: Rendiconti (V) 20 (1911), 10-16.

  66. Harriot and binary numbers
    • Laplace wrote:- .

  67. Early Maths in America
    • Adrain is known for his apparently independent discovery of the law of distribution of errors; Bowditch is known for his translation of Laplace's 'Mecanique Celeste' accompanied by a commentary of his own; and Peirce is now known chiefly for his classical memoir, 'Linear Associative Algebra,' which was the first important research made by an American in the field of pure mathematics.

  68. Dubreil-Jacotin on Mary Somerville
    • Mary Somerville's principal work consisted of translating and thus making known to her contemporaries the celestial mechanics of Laplace and of adding to it personal notes of real value.

  69. R A Fisher: 'Statistical Methods' Introduction
    • Three of the distributions with which we shall be concerned, Bernoulli's binomial distribution, Laplace's normal distribution, and Poisson's series, were developed by writers on probability.

  70. Percy MacMahon addresses the British Association in 1901
    • Whereas in 1801 on the Continent there were the leaders Lagrange, Laplace and Legendre, and of rising men, Fourier, Ampere, Poisson and Gauss, we could only claim Thomas Young and Ivory as men who were doing notable work in research.

  71. Peres books
    • Nowhere, perhaps, would it be more legitimate to speak of a Greek miracle." The following chapters deal successively with the progress made up to Newton exclusively; from the period of Newton to Euler, which represents the science of the eighteenth century, and then of the period from 1780 to 1860, which was that of the great French geometers: Lagrange, Laplace, Legendre, Gauchy, Galois, and which is also brilliantly illustrated by the German school with Gauss, Jacobi, Riemann, Weierstrass, the latter being connected, however, rather with the contemporary movement.

  72. Keynes: 'Probability' Introduction Ch II
    • [This view has often been taken, e.g., by Bernoulli and, incidentally, by Laplace; also by Fries (see Czuber, Entwicklung, p.

  73. Craig books
    • The names of Euler, Lagrange and Laplace in the last century, and of Helmholtz, Stokes, Thomson, Rayleigh and Kirchhoff in this, stand out predominantly as those that have done the most to advance the theory to its present position.

  74. Science at St Andrews
    • He contributed to the history of gravitation as it was shaping under Colin Maclaurin, Lagrange and Laplace, on the foundation of Newton's Principia.

  75. The French Statistical Society
    • As for the third year, this award is replaced by a tribute - the Pierre Simon de Laplace Prize - given to an established statistician whose contribution to French-speaking statistics is particularly outstanding.

  76. Magnus books
    • Laplace transforms are almost unique in that several up-to-date and thoroughly satisfactory tables of such transforms are available.

  77. Goursat: 'Cours d'analyse mathématique
    • - Methode de Laplace.

  78. Leonard J Savage: 'Foundations of Statistics
    • It was pushed forward in the nineteenth century by Laplace, Gauss, and others, and it has been subject to a fervour of activity since the early twenties of this century, when it received great impetus from the work of R A Fisher.

  79. Who was who 1852
    • J L Lagrange (1736-1813) spent the last twenty years of his wandering life in France, men like J Fourier (1768-1830), P S Laplace (1749-1827), A M Legendre (1752-1833) and S D Poisson (1781-1840) brought French mathematics to new heights.

  80. Library of Mathematics
    • Solutions of Laplace's equationD R Bland .

  81. Airy on Thales' eclipse
    • The great step made in theory, in reference to these inquiries, was the discovery made by Laplace near the end of the last century, of the secular change in the moon's mean motion in longitude (accompanied by similar changes in the motion of the perigee and the node).

  82. Chini publications
    • Mineo Chini, Teoria della equazione di Laplace.

  83. Solve Applied Problems
    • Although the subjects of Fourier series, Fourier and Laplace transforms, and integral equations, are not strictly applied mathematics, they are essential for the study of wave motions, including vibrating strings, sound waves and water waves, and for the study of heat conduction.

  84. Bertrand's work on probability' Introduction
    • Bertrand mentioned some of his predecessors (De Moivre, Laplace, Bienayme), but did not refer to other scholars, notably to Chebyshev.

  85. Edward Sang on his tables
    • Laplace had, in anticipation, reduced all his data in the Mecanique Celeste to the new system, and instruments had been graduated suitably.


  1. Quotations by Laplace
    • Quotations by Pierre-Simon Laplace .
    • Laplace: Sire, I had no need of that hypothesis.

  2. Quotations by Ball
    • Biot, who assisted Laplace in revising it [Mecanique Celeste] for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, 'Il est aise a voir' [it is easy to see].
    • The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries.
    • Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one.
    • Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.

  3. A quotation by Bowditch
    • I never came across one of Laplace's Thus it plainly appears without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how in plainly appears.

  4. Quotations by Lagrange
    • One day after [Laplace] had invited Lagrange to dinner, Lagrange asked: "Will it be necessary to wear the costume of a senator?" in a mocking tone, of which everyone sensed the malice, except the amphityron [=host] senator.

  5. Quotations by Arago
    • Eulogy on Laplace .

  6. A quotation by Mises
    • The unlimited extension of the validity of the exact sciences was a characteristic feature of the exaggerated rationalism of the eighteenth century" (in reference to Laplace).

  7. Quotations by Gauss
    • Sin2 φ is odious to me, even though Laplace made use of it; should it be feared that sin2 φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ2), well then, let us write (sin φ)2, but not sin2 φ, which by analogy should signify sin (sin φ) .

Famous Curves

  1. Frequency
    • It was also studied with Laplace and Gauss.

  2. Lissajous
    • His New American Practical Navigator (1802) and his translation of Laplace's Mecanique celeste gave him an international reputation.


  1. Mathematical Chronology
    • Euler, Lagrange and Laplace also work on the three-body problem.
    • Laplace presents his famous nebular hypothesis in Exposition du systeme du monde which views the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
    • Laplace publishes the first volume of five-volume Traite de mecanique celeste (Celestial Mechanics).
    • Laplace publishes the two volumes of Theorie Analytique des probabilites (Analytical Theory of Probabilities).
    • The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.
    • Inspired by the work of Laplace, Adrain publishes Investigation of the figure of the Earth and of the gravity in different latitudes.
    • This puts in doubt the stability proofs of the solar system given by Lagrange and Laplace.
    • Bateman applies Laplace transforms to integral equations.

  2. Chronology for 1810 to 1820
    • Laplace publishes the two volumes of Theorie Analytique des probabilites (Analytical Theory of Probabilities).
    • The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.
    • Inspired by the work of Laplace, Adrain publishes Investigation of the figure of the Earth and of the gravity in different latitudes.

  3. Chronology for 1780 to 1800
    • Laplace presents his famous nebular hypothesis in Exposition du systeme du monde which views the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
    • Laplace publishes the first volume of five-volume Traite de mecanique celeste (Celestial Mechanics).

  4. Chronology for 1900 to 1910
    • Bateman applies Laplace transforms to integral equations.

  5. Chronology for 1890 to 1900
    • This puts in doubt the stability proofs of the solar system given by Lagrange and Laplace.

  6. Chronology for 1740 to 1760
    • Euler, Lagrange and Laplace also work on the three-body problem.

EMS Archive

  1. Edinburgh Mathematical Society Lecturers 1883-2016
    • (University College, London) Transformations of axes for Whittaker's solution of Laplace's equation, {Communicated by Edward Blades} .
    • A form of Laplace's operator, {Communicated by Edward Thomas Copson} .
    • (Edinburgh) Note on Whittaker's solution for Laplace's equation .
    • (Edinburgh) On the 'Elementary' solution of a Laplace's equation .
    • (Edinburgh) Generalised solutions of Laplace's equation .
    • (Edinburgh) Symbolic representation of the Laplace transformation; .
    • (Edinburgh) The life and work of Laplace .
    • (London) Heat kernel bounds for Laplace-Beltrami operators and subelliptic operators on manifolds .

  2. EMS Ince
    • He gave first the derivation of Lame's differential equation in its algebraic and Jacobian forms by the consideration of Laplace's equation in confocal coordinates.
    • He showed that the most appropriate notation for the Lame polynomials is based on (a) their degree, and (b) the number of their zeros in a multiple period, since this classification (unlike that of Laplace) is also appropriate for Lame functions in general.

  3. EMS 1938 Colloquium
    • He sketched the views of Laplace, de Mises, Wald and others, and described in more detail the "modernised classical definition" of Neyman and Kolmogorov.
    • The discussion was noteworthy for Professor Whittaker's vigorous defence of the classical (Laplace's) point of view against all comers.

  4. EMS Proceedings papers
    • Transformations of axes for Whittaker's solution of Laplace's equation .

  5. EMS Proceedings papers
    • Note on Whittaker's solution for Laplace's equation .

  6. 1916-17 Mar meeting
    • Jeffery, G B: "Transformations of axes for Whittaker's solution of Laplace's equation", {Communicated by Edward Blades} .

  7. 1930-31 Dec meeting
    • Ruse, H S: "Generalised solutions of Laplace's equation", [Proceedings, Vol.

  8. 1929-30 Jun meeting
    • Ruse, H S: "On the 'Elementary' solution of a Laplace's equation", [Proceedings, Vol.

  9. 1922-23 Jan meeting
    • King, A W: "A form of Laplace's operator", [Title] {Communicated by Edward Thomas Copson} .

BMC Archive

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Gazetteer of the British Isles

  1. References
    • Laplace in Calvados.
    • Laplace.

  2. London individuals S-Z
    • Mary Somerville (1780-1872), translator of Laplace's Mecanique Celeste and populariser of science lived at 12 Hanover Square (on the north side).
    • In 1716-1718, he produced six issues of the first scientific journal in Swedish; in 1716-1747, he served on Sweden's Board of Mines, working as a mining engineer, civil engineer, geologist and a promoter of new techniques, also writing on these topics and cosmology (showing that the earth had slowed down and advancing a nebular hypothesis which influenced Buffon, Kant and Laplace, etc.), chemistry (suggesting that crystals were like lattices of spheres), mineralogy, metallurgy, anatomy and physiology, etc.; in 1718, he wrote a booklet on the octal number system; his Regel-Konsten of 1718 was the first Swedish algebra book; in 1718, he published a method of finding longitude from the moon which was revised and extended several times, then submitted to the Board of Longitude in 1766, when Maskelyne rejected it; in 1719, he advocated the use of decimal measures and coinage and proposed a water tank for testing stability of model ships.

  3. Nottingham, Nottinghamshire
    • Toplis was an enthusiast for Leibnizian calculus and continental mathematics and had translated the first book of Laplace's Mecanique Celeste and published it himself in Nottingham in 1814.

  4. Cambridge Individuals
    • He was an enthusiast for the new continental calculus--he translated the first book of Laplace's Mecanique Celeste and published it himself in 1814, in Nottingham where he was head of the Free Grammar School in 1806-1819.

  5. Other London Institutions outside the centre
    • Over the central portico and on the parapet of the facade are statues of Archimedes, Aristotle, Bacon, Bentham, Cuvier, Davy, Galen, Galileo, Goethe, Harvey, Hume, Hunter, Laplace, Leibniz, Linnaeus, Lock, Newton, Plato, Adam Smith, and a few non-scientists.

  6. London individuals H-M
    • Heaviside also developed the operational calculus, now partially formalised in the standard theory of Laplace transforms, though Heaviside's approach is considerably more sophisticated and general.

Astronomy section

  1. Extras Index

  2. The Dynamics of the Solar System
    • Thankfully, Laplace realised that in fact it was the earth's spin that was gradually slowing.
    • Laplace also theorised that our solar system was formed by gas clouds condensing.

  3. List of astronomers

  4. List of astronomers
    • Laplace, Pierre-Simon .

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