- Timeline of calculus and mathematical analysis
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timeline ofcalculus andmathematical analysis 1000 to 1500
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1020 —Abul Wáfa — Discussed the quadrature of theparabola and the volume of theparaboloid .
*1021 —Ibn al-Haytham completes his "Book of Optics ", which formulated and solved “Alhazen's problem” geometrically, and developed and proved the earliest general formula forinfinitesimal andintegral calculus usingmathematical induction .
*1100s — Bhaskara Acharya conceivesdifferential calculus , and also developsRolle's theorem ,Pell's equation , a proof for thePythagorean Theorem , proves that division by zero is infinity, computes π to 5 decimal places, and calculates the time taken for the earth to orbit the sun to 9 decimal places
*1300s — Madhava is considered the father ofmathematical analysis , who also worked on the power series for p and for sine and cosine functions, and along with otherKerala school mathematicians, founded the important concepts ofCalculus
*1300s —Parameshvara , aKerala school mathematician, presents a series form of thesine function that is equivalent to itsTaylor series expansion, states themean value theorem ofdifferential calculus , and is also the first mathematician to give the radius of circle with inscribedcyclic quadrilateral
*1400 — Madhava discovers the series expansion for the inverse-tangent function, the infinite series for arctan and sin, and many methods for calculating the circumference of the circle, and uses them to compute π correct to 11 decimal places16th century
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1501 —Nilakantha Somayaji writes the “Tantra Samgraha”, which lays the foundation for a complete system of fluxions (derivatives), and expands on concepts from his previous text, the “Aryabhatiya Bhasya”.
*1550 —Jyeshtadeva , aKerala school mathematician, writes the “Yuktibhasa”, the world's firstcalculus text, which gives detailed derivations of many calculus theorems and formulae.17th century
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1629 - Pierre de Fermat develops a rudimentarydifferential calculus ,
*1634 -Gilles de Roberval shows that the area under acycloid is three times the area of its generating circle,
*1658 -Christopher Wren shows that the length of acycloid is four times the diameter of its generating circle,
*1665 -Isaac Newton works on thefundamental theorem of calculus and develops his version ofinfinitesimal calculus ,
*1671 - James Gregory develops a series expansion for the inverse-tangent function (originally discovered by Madhava)
*1673 -Gottfried Leibniz also develops his version ofinfinitesimal calculus ,
*1675 - Isaac Newton invents anNewton's method for the computation of functional roots,
*1691 - Gottfried Leibniz discovers the technique of separation of variables for ordinarydifferential equation s,
*1696 - Guillaume de L'Hôpital states his rule for the computation of certain limits,
*1696 -Jakob Bernoulli andJohann Bernoulli solve brachistochrone problem, the first result in thecalculus of variations ,18th century
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1712 -Brook Taylor developsTaylor series ,
*1730 - James Stirling publishes "The Differential Method",
*1734 -Leonhard Euler introduces theintegrating factor technique for solving first-order ordinarydifferential equation s,
*1735 - Leonhard Euler solves theBasel problem , relating an infinite series to π,
*1739 - Leonhard Euler solves the generalhomogeneous linear ordinary differential equation withconstant coefficients ,
*1748 -Maria Gaetana Agnesi discusses analysis in "Instituzioni Analitiche ad Uso della Gioventu Italiana",
*1762 -Joseph Louis Lagrange discovers thedivergence theorem ,19th century
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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 theintermediate value theorem ---acontinuous 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 theCauchy integral theorem for integration around the boundary of a rectangle in thecomplex plane ,
*1825 - Augustin-Louis Cauchy presents theCauchy integral theorem for general integration paths -- he assumes the function being integrated has a continuous derivative, and he introduces the theory of residues incomplex analysis ,
*1825 - André-Marie Ampère discoversStokes' theorem ,
*1828 - George Green provesGreen'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 theLaurent 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 provesStokes' theorem ,
*1873 -Georg Frobenius presents his method for finding series solutions to linear differential equations withregular singular point s,20th century
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1908 -Josip Plemelj solves the Riemann problem about the existence of a differential equation with a givenmonodromic group and uses Sokhotsky - Plemelj formulae,
*1966 -Abraham Robinson presentsNon-standard analysis .
*1985 -Louis de Branges de Bourcia proves theBieberbach conjecture ,
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