Από το Νεύτωνα στον Weierstrass

Από το Νεύτωνα στον Weierstrass

Weierstrass Newton, Isaac (1642-1727) Nature and Natures laws lay hid in

night; God said, Let Newton be! And all was Light. To (fluxions) ( ) ( )

Barrow Barrow Wallis

: (Wallis) (Barrow) (Gregory Wallis) De analysi per aequationes numero terminorum infinitas 1669 1711 ethodus fluxionum et serierum infinitorum. X. 1671, 1736 , .

Tractatus de Quadratura Curvarum 1693 (fluxions) : . x . y x y (fluents flowing quantities) y x y x

. . 1693: Tractatus de Quadratura Curvarum : x x+o xn (x+o)n xn + noxn-1 + (nn-n)/2 ooxn-2 + . .

Principia (1687) , , Godefried Wilhem Leibniz

(1646 1716) Huyghens Barrow Wallis 1684: Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractals nec irrationales quantitates moratur, et singulare pro illis calculi genus Acta Eruditorum .

Leibniz x y dx, dy : H dy/dx d Calculus summatorius: y2 ydy 2

y=x2 dy=d(x2)=(x+dx)2-x2=2xdx+(dx)2 2x= Methodus tangentium inversa, seu de functionibus ( ): y y

Newton . x,y Leibniz x y.

. T dx, dy . H 1664-1666: Woolsthorpe: Newton . 1666. 1713: Newton

. Henry Oldenberg o Leibniz Newton. 16821684: Leibniz Acta Eruditorum 1710: Leibniz

O Bernoulli Jakob (1654-1705) Johann (1667 1748) Bernoulli Johann Jakob .

. . : x = at - h sin(t), y = a - h cos(t) (Catenary) ;

: Johann, Leibniz, Huyghens . y = a cosh(x/a) M Guillaume de L'Hospital (1661-1704) 1696:

. - Johann Bernoulli Leibniz . George Berkeley (1685- 1753)

The Analyst; or, A Discourse Addressed to an Infidel Mathematician. London, Tonson, 1734 Berkeley . Berkley

: ; ( ;).

Edmund Halley (1656-1742) 1784:

Simon L Huilier . Joseph Louis Lagrange (1736-1813) Mecanique analytique (1788): f

Leonhard Euler (1707-1783) 1748: . .

1734: O Euler 2 2 2 ... S 2 2 6 1 2 3 1

1 1 S p 1

p 1 p S p p (; ;) . 1979, R. Apery: To S3 Jean le Rond D Alembert

1717 - 1783 , . Encyclopedie 1765 Jean le Rond D Alembert 1717 - 1783 !

! (fnctions primitives) .

. Augustin Louis Cauchy :

f ( x i) f ( x ) : f ( x ) lim i 0 i ... Louis Cauchy (1789-1857)

Carl Friedrich Gauss (1777-1855) Bernhard Riemann, (1826-1866)

Weierstrass, Karl (1815--1897) .

. Cauchy: . Weierstrass: . 1791: Louis Francois Arbogast (1759 1803):

1817: Bernhard Bolzano (17811848): . . 1822: Joseph Fourier (1768 -1830)

Theorie Analytique de la Chaleur Weierstrass von Koch

( 4/3) Helge von

Koch 1870-1924 Hilbert Peano Giuseppe Peano 1858 - 1932 Waclaw Sierpinski 1882-1969

Sierpinski - Sierpinski

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