A hisotry of two theorems of calculus: M. Rolle, B. Bolzano, A. Cauchy

Galina Iwanowna Sinkiewicz. "A hisotry of two theorems of calculus: M. Rolle, B. Bolzano, A. Cauchy." Antiquitates Mathematicae 7 (2013): null. <http://eudml.org/doc/293249>.

@article{GalinaIwanownaSinkiewicz2013,
abstract = {The paper is devoted to a story of the well-known Rolle's theorem: If the function is continuous on [a, b], differentiable in  (a, b)  and  f (a) = f (b), then  there exists in  (a, b ) at least one point  c  such that f'(c) = 0. A history of the associated statements about the roots of a continuous function: If the function  f  is continuous on  [a, b]  and has different signs at the ends of the interval, then in  (a, b) there is at least one point  c such that  f (c) = 0. This theorem in the twentieth century has been called the Bolzano-Cauchy's theorem.},
author = {Galina Iwanowna Sinkiewicz},
journal = {Antiquitates Mathematicae},
keywords = {history of mathematics, history of science, calculus},
language = {eng},
pages = {null},
title = {A hisotry of two theorems of calculus: M. Rolle, B. Bolzano, A. Cauchy},
url = {http://eudml.org/doc/293249},
volume = {7},
year = {2013},
}

TY - JOUR
AU - Galina Iwanowna Sinkiewicz
TI - A hisotry of two theorems of calculus: M. Rolle, B. Bolzano, A. Cauchy
JO - Antiquitates Mathematicae
PY - 2013
VL - 7
SP - null
AB - The paper is devoted to a story of the well-known Rolle's theorem: If the function is continuous on [a, b], differentiable in  (a, b)  and  f (a) = f (b), then  there exists in  (a, b ) at least one point  c  such that f'(c) = 0. A history of the associated statements about the roots of a continuous function: If the function  f  is continuous on  [a, b]  and has different signs at the ends of the interval, then in  (a, b) there is at least one point  c such that  f (c) = 0. This theorem in the twentieth century has been called the Bolzano-Cauchy's theorem.
LA - eng
KW - history of mathematics, history of science, calculus
UR - http://eudml.org/doc/293249
ER -