18th ce of math emetics
TRANSCRIPT
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The 18th CE Mathematics of
France:
The Development of Analysis
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The 18th century marks from 1701 to 1800 in
the Gregorian calendar.
Age of Reason and Change
it is known as the medieval period
1700's was the times to develop the calculus
and to expand the analysis made in 1600's.
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there were so many enlargements of thedesign trigonometry, the analytic geometry,the number theory, the equation theory, the
probability theory, the differential equation,and the analytic dynamics and also so manynew creations of the insurance statistics, thefunction of higher degree, the partialdifferential equation, the descriptivegeometry and the differential geometry.
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Most of the late 17th Century and a good part
of the early 18th were taken up by the work
of disciples of Newton and Leibniz, who
applied their ideas on calculus to solving a
variety of problems in physics, astronomy andengineering.
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BERNOULLIBROTHERS(Jacob and JohannBernoulli)
*Jacob Bernoulli
Became professor in
Basel University.
calculus of variations.
the Ars conjectandi, was
published in 1713.
Bernoulli distribution and
Bernoulli theorem of statistics
and probability theory;
died from Tuberculosis.
Jacob (1654-1705) andJohann
Bernoulli (1667-1748)
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Johann Bernoulli
he became Professor in Basel,Switzerland and at that time,
Leonard Euler was one of his student.
famous rule about 0 0 (a problem which had dogged
mathematicians since Brahmagupta's initial work on the rules for
dealing with zero back in the 7th Century).
he improved the work of his brother and he named Bernoulli
equation, He used the word 'integral' for the first time in 1690.
He greatly enriched the calculus.
asl'Hospital's rule-with the help of Marquis de l'Hospital
(1661~1704), he was able to arrange the first book in 1696 calledthe first calculus textbook.
had 3 sons namely Nicolaus (1695-1726), Daniel(1700-1782),
and Johann II (1710-1790),
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Abraham De Moivre(16671754)
French mathematical prodigy.noted for his workAnnuities
upon Lives, which played an
important role in the history of
actuarial mathematics,.In his book ofDoctrine of
Chances, which contained much
new material on the theory of
probability,and his Miscellanea
analytica.
de Moivre's formula,
(cosx+ isinx)n = cos(nx) + isin(nx),
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De Moivres formula
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Comte de Buffon(1707-1788,)
the first example of a
geometrical probability, hisfamous "needle problem" for
experimentally approximating the
value of .
he introduced differential and
integral calculus into probability
theory compiled in his book
named Sur le jeu de franc-
carreau
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Geometrical Probability involving
Calculus
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BrookTaylor(1685-1731)
English mathematician
Taylor's theorem and
theTaylor series.
The Incrementorum Directa
etInversa (1715) added a
new branch to the higher
mathematics, he designatedthe "calculus of finite
differences.
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TaylorsSeries
TaylorsTheorem
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Colin Maclaurin(1698-1746)
Scottish mathematician whomade important contributions to
geometry and algebra.
he also introduced Maclaurin
series like Taylor series. series to characterize maxima,
minima, and points of inflection
for infinitely differentiable
functions.
he study of elliptic integrals
reducing many intractable
integrals to problems of finding
arcs for hyperbolas.
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TaylorsSeriesExpansion
Taylor series expansion represents
an analytic functionf(x) as an infinite
sum of terms around the expansion
point x=a:
Maclaurin SeriesExpansion
Taylor series expansion around
x
=0 iscalled Maclaurin series expansion
Taylor series expansion requires a
function to have derivatives up to
infinite order around the expansionpoint.
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Mathematician
of Revolution Ages
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Joseph LouisLagrange (1736-
1813)
French mathematician
Mecanique analytique -
aeneral equations of motion of
a dynamical system known
today as Lagrange's equations.
Lagrange's theorem
differential equations andnumber theory.
published his work,
Miscellanea Taurinensia.
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Pierre-Simon Laplace(1749-1827)
French Mathematician and
Astronomer
Mcanique
Cleste (Celestial Mechanics)
restated the nebular
hypothesis of the origin of
the solar system .
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he started to work on differential
equations and finite differences .
His work entitled Mmoire sur la probabilit
des causes par les vnements was published
in 1774.
Spherical harmony and inductive probabi.lity
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Adrien-Marie Legendre(1752-1833)
French mathematician
he is known for Legendretransformation and ellipticfunctions
he worked on the rootsof polynomials
lments degomtrie, published in 1874
noted for his quadraticrecprocity
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Gaspard Monge(1746-1818)
French mathematician,
inventor of descriptive
geometry.
he published "Sur la thoriedes dblais et des
remblais and Trait
lmentaire de la statique
gives the ordinary differentialequation of the curves of
curvature,
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The Metric System
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The word 'meter' is from the Greek word 'metron', whichmeans 'a measure'. At the time the metric system wasbeing defined, there were two competing approaches tothe definition of the length of the meter. The initialsuggestion was that it be the length of 'a pendulumhaving a half-period of one second'. The alternativeapproach was to set it to one ten-millionth of 'the lengthof the earth's meridian along a quadrant'. Specifically,one ten-millionth of the distance from the North Pole tothe equator, along the meridian running near Dunkirk inFrance. The French Academy of Science, which was
tasked with developing the metric system, decided onthe latter approach in 1991 (on the basis that the formerapproach does not give a consistent measure, as slightvariations in the earth's gravity from one place toanother would result in different values).
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The metric system is a system of units formeasurement developed in late 18th century
France by the chemist Lavoisier to replace thedisparate systems of measures then in use with aunified, natural and universal system. In the earlymetric system there were several fundamental orbase units, the grad or grade for angles, themetre for length, the gram for weight and thelitre for capacity. These were derived from eachother via the properties of natural objects, mainlywater: 1 litre of water weighs 1 kg and measures
1 cubic decimetre (dm). Other units werederived from this, such as the Celsiustemperature scale, where water freezes as 0Cand boils as 100C.
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Measurements of length, area, volume, and
weight play an important part in the practical
applications of mathematics, Basic among the
units of these measurements is that of length,
for given a unit of length, units for the other
quantities can easily be devised.
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