Timeline of calculus and mathematical analysis explained
A timeline of calculus and mathematical analysis.
500BC to 1600
,
,
,
,
and
[6] [7] This theory is now well known in the Western world as the
Taylor series or infinite series.
[8] - 14th century - Parameshvara discovers a third order Taylor interpolation for
,
- 1445 - Nicholas of Cusa attempts to square the circle,
- 1501 - Nilakantha Somayaji writes the Tantrasamgraha, which contains the Madhava's discoveries,
- 1548 - Francesco Maurolico attempted to calculate the barycenter of various bodies (pyramid, paraboloid, etc.),
- 1550 - Jyeshtadeva writes the Yuktibhāṣā, a commentary to Nilakantha's Tantrasamgraha,
- 1560 - Sankara Variar writes the Kriyakramakari,
- 1565 - Federico Commandino publishes De centro Gravitati,
- 1588 - Commandino's translation of Pappus' Collectio gets published,
- 1593 - François Viète discovers the first infinite product in the history of mathematics,
17th century
- 1606 - Luca Valerio applies methods of Archimedes to find volumes and centres of gravity of solid bodies,
- 1609 - Johannes Kepler computes the integral
,
- 1611 - Thomas Harriot discovers an interpolation formula similar to Newton's interpolation formula,
- 1615 - Johannes Kepler publishes Nova stereometria doliorum,
- 1620 - Grégoire de Saint-Vincent discovers that the area under a hyperbola represented a logarithm,
- 1624 - Henry Briggs publishes Arithmetica Logarithmica,
- 1629 - Pierre de Fermat discovers his method of maxima and minima, precursor of the derivative concept,
- 1634 - Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle,
- 1635 - Bonaventura Cavalieri publishes Geometria Indivisibilibus,
- 1637 - René Descartes publishes La Géométrie,
- 1638 - Galileo Galilei publishes Two New Sciences,
- 1644 - Evangelista Torricelli publishes Opera geometrica,
- 1644 - Fermat's methods of maxima and minima published by Pierre Hérigone,
,
,
and
(originally discovered by
Madhava),
- 1670 - Isaac Barrow publishes Lectiones Geometricae,
- 1671 - James Gregory rediscovers the power series expansion for
and
(originally discovered by
Madhava),
notation for integrals,
18th century
- 1711 - Isaac Newton publishes De analysi per aequationes numero terminorum infinitas,
- 1712 - Brook Taylor develops Taylor series,
- 1722 - Roger Cotes computes the derivative of sine function in his Harmonia Mensurarum,
- 1730 - James Stirling publishes The Differential Method,
- 1734 - George Berkeley publishes The Analyst,
- 1734 - Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,
- 1735 - Leonhard Euler solves the Basel problem, relating an infinite series to π,
- 1736 - Newton's Method of Fluxions posthumously published,
- 1737 - Thomas Simpson publishes Treatise of Fluxions,
- 1739 - Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients,
- 1742 - Modern definion of logarithm by William Gardiner,
- 1742 - Colin Maclaurin publishes Treatise on Fluxions,
- 1748 - Euler publishes Introductio in analysin infinitorum,
- 1748 - Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,
- 1762 - Joseph Louis Lagrange discovers the divergence theorem,
- 1797 - Lagrange publishes Théorie des fonctions analytiques,
19th century
- 1807 - Joseph Fourier announces his discoveries about the trigonometric decomposition of functions,
- 1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,
- 1815 - Siméon Denis Poisson carries out integrations along paths in the complex plane,
- 1817 - Bernard Bolzano presents the intermediate value theorem — a continuous function which is negative at one point and positive at another point must be zero for at least one point in between,
- 1822 - Augustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle in the complex plane,
- 1825 - Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths—he assumes the function being integrated has a continuous derivative, and he introduces the theory of residues in complex analysis,
- 1825 - André-Marie Ampère discovers Stokes' theorem,
- 1828 - George Green introduces Green's theorem,
- 1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,
- 1841 - Karl Weierstrass discovers but does not publish the Laurent expansion theorem,
- 1843 - Pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem,
- 1850 - Victor Alexandre Puiseux distinguishes between poles and branch points and introduces the concept of essential singular points,
- 1850 - George Gabriel Stokes rediscovers and proves Stokes' theorem,
- 1861 - Karl Weierstrass starts to use the language of epsilons and deltas,
- 1873 - Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points,
20th century
Notes and References
- Web site: History of the Calculus -- Differential and Integral Calculus . 2022-11-03 . www.edinformatics.com.
- Web site: Plummer . Brad . 2006-08-09 . Modern X-ray technology reveals Archimedes' math theory under forged painting . 2022-11-03 . Stanford University . en.
- Ossendrijver . Mathieu . Jan 29, 2016 . Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph . Science . 10.1126/science.aad8085 . 26823423 . 351 . 6272 . 482–484 . 206644971 .
- Web site: On Squares, Rectangles, and Square Roots - Square roots in ancient Chinese mathematics Mathematical Association of America . 2022-11-03 . www.maa.org.
- Web site: Conic Sections: A Resource for Teachers and Students of Mathematics . 2022-11-03 . jwilson.coe.uga.edu.
- Web site: Weisstein . Eric W. . Taylor Series . 2022-11-03 . mathworld.wolfram.com . en.
- August 1932 . The Taylor Series: an Introduction to the Theory of Functions of a Complex Variable . Nature . en . 130 . 3275 . 188 . 10.1038/130188b0 . 1932Natur.130R.188. . 4088442 . 1476-4687. free .
- Web site: Saeed . Mehreen . 2021-08-19 . A Gentle Introduction to Taylor Series . 2022-11-03 . Machine Learning Mastery . en-US.