math in 18th century

 Euler worked in almost all areas of mathematics: geometry, calculus, trigonometry, algebra,applied mathematics, graph theory and number theory, as well as , lunar theory, optics and

 In 18th century mathematics is

already a modern science

 Mathematics begins to develop very fast because of introducing it to

schools

 Therefore everyone have a chance to learn the basic learnings of

mathematics

 Thanks to that, large number of new mathematicians appear on stage

 There are many new ideas, solutions

FAMOUS MATHEMATICIANS

LEONHARD EULER

Leonhard Paul Euler

(1707-1783)

 He was a Swiss mathematician

 Johann Bernoulli made the biggest

influence on Leonhard

 1727 he went to St Petersburg where

he worked in the mathematics

department and became in 1731 the head of this department

 1741 went in Berlin and worked in

Berlin Academy for 25 years and after that he returned in St Ptersburg

where he spent the rest of his life.



 Euler worked in almost all areas of

mathematics: geometry, calculus,

trigonometry, algebra,applied mathematics,

graph theory and number theory, as well as , lunar theory, optics and other areas of

physics

 He introduced several notational conventions

in mathematics

 Concept of a function as we use today was

introduced by him;he was the first

mathematician to write f(x) to denote function

 He also introduced the modern notation for

the trigonometric functions, the letter e for the base of the natural logarithm (now also known

as Euler’s number), the Greek letter Σ for

summations and the letter i to denote the

imaginary unit

 He wrote 45 books an over 700 theses.

 His main book is Introduction in Analisyis of the Infinite.

 He discovered ways to express

various logarithmic functions using power series, and he successfully

defined logarithms for negative and complex numbers

 He also defined the exponential

function for complex numbers, and discovered its relation to the

trigonometric functions

EULER’ S FORMULA For any real number

Number theory

 He contributed significantly to the

theory of perfect numbers, which had fascinated mathematicians since

Euclid.

 His prime number theorem and the

law of quadratic reciprocity are

regarded as fundamental theorems of number theory.

 Euler (1765) showed that in any triangle, the orthocenter, circumcenter, centroid, and

nine-point center are

collinear.

 Because of that the line

which connects the points

above is called Euler line.

Seven bridges of Konigsberg

 This was old mathematical problem.

 The problem was to decide whether it

is possible to follow a path that

crosses each bridge exactly once and returns to the starting point

 1736 Euler solved this problem, and prooved that it is not possible.

 This solution is considered to be the first theorem of graph theory

 Euler was very importnat for further development of mathematics

 Next quotation tells enough about his importance:

 “Lisez Euler, lisez Euler, c'est notre

maître à tous ”(Read Euler, read

Euler, he is the master of us all.)

Pierre-Simon Laplace

GABRIEL CRAMER

 He is the most famous by his rule

(Cramer’s rule) which gives a solution

of a system of linear equations using determinants.

THOMAS SIMPSON

 He received little formal education

and taught himself mathematics while

he was working like a weaver.

 Soon he became one of the most

distinguished members of the English school

 Simpson is best remembered for his

work on interpolation and numerical methods of integration

 He wrote books Algebra, Geometry,

Trigonometry, Fluxions, Laws of

Chance, and others

THOMAS SIMPSON

(1710-1761)

JEAN LE ROND D’ALAMBERT

 He dealt with problems of dinamics

and fluids and especially with problem

of vibrating string which leads to

solving partial diferential equations

 During his second part of life, he was mainly occupied with the great French encyclopedia

JEAN LE ROND D’ALAMBERT

(1717-1783)

For this he wrote the introduction, and numerous philosophical and

mathematical articles; the best are

those on geometry and on

probabilities.

JOSEPH LOUIS LANGRANGE

 He didn’t show any intersts for

mathematics untill his 17.

 From his 17, he alone threw himself into mathematical studies

 Already with 19, he wrote a letter to Euler in which he solved the

isoperimetrical problem which for

more than half a century had been a subject of discussion.

JOSEPH LOUIS LANGRANGE

(1736-1813)

 Lagrange established a society known

as Turing Academy, and published

Miscellanea Taurinesia, his work in

which he corrects mistakes made by

some of great mathematicians

 He was studing problems of analytical geometry, algebra, theory of numbers, differential eqations, mechanics,

astronomy, and many other

 Napoleon named Lagrange to the

Legion of Honour and made him the

Count of the Empire in 1808

 On 3 April 1813 he was awarded the Grand Croix of the Ordre Impérial de

la Réunion He died a week later

PIERRE SIMON LAPLACE

 French mathematician and astronomer

mecanique celeste and Theory analytique des probabiliteis

“Laplace transform” and with the

“Laplace ex pansion” of a determint

postulate the existence of black holes

have their name engraved on Eiffel

Tower

PIERRE-SIMON LAPLACE

(1749-1827)

 It is also interesting to say the

difference between Laplace and

Lagrange

 For Laplace, mathematics was merely

a kit of tools used to explain nature

 To Lagrange, mathematics was a

sublime art and was its own excuse for being

GASPARD MONGE

 French mathematician also known as Comte de Péluse

 Monge is considered the father of

differential geometry because of his work Application de l'analyse à la

géométrie where he introduced the concept of lines of curvature of a

surface in 3-space

GASPARD MONGE

(1746-1818)

 His method, which was one of cleverly representing 3-dimensional objects by appropriate projections 2-dimensional plane, was adopted by the military

and classified as top secret

ADRIEN – MARIE LEGENDRE

 He made important contributions to

statistics, number theory, abstract

algebra and mathematical analysis

 Legendre is known in the history of

elementary methematics principially

for his very popular Elements de

geometrie

 He gave a simple proof that π(pi) is

irrational as well as the first proof that π2(pi squared) is irrational

ADRIEN – MARIE LEGENDRE

(1752-1833)

JEAN BAPTISTE JOSEPH

FOURIER

 French mathematician,

physicist and historian

 He studied the mathematical theory of heat conduction.

JEAN BAPTISTE JOSEPH FOURIER

(1768-1830)

Fourier established the partial differential

equation governing heat diffusion and solved in by using infinite series of

trigonometric functions

JOHANN CARL FRIEDRICH GAUSS AUSS

JOHANN CARL FRIEDRICH GAUSS AUSS

(1777 – 1855)

 He worked in a wide variety of fields

in both mathematics and physics

incuding number theory, analysis,

differential geometry, geodesy,

magnetism, astronomy and optics.

 “Mathematics is the queen of the

sciences and number theory is the

queen of mathematics.”

AUGUSTIN LOUIS CAUCHY

 Cauchy started the project of

formulating and proving the teorems

of calculus in a rigorous manner and was thus an early pioneer of analysis

 He also gave several important

theorems in complex analysis and

initiated the study of permutation

groups

AUGUSTIN LOUIS CAUCHY

(1789-1857)

 He also researched in convergence

and divergence of infinite series,

differential equations, determinants, probability and mathematical physics

 He was first to prove Taylor’s

theorem, he brought a whole new set

of teorems and definitions, he dealed with mechanics, optics, elasticity and many other problems

 His last words were:

“Men pass away, but their deeds

abide.”

Anela Bocor Mateja Jelušić

Ivan Jelić Vojislav Đuračković

Boris Dokić