8 Introduction to Celebrities in Fluid Mechanics
599
inequality to describe the limit process. Nowadays, all calculus textbooks still
use the definitions of limit, continuity, derivative, convergence, which were
put forward by Cauchy et al. His explanation of calculus was widely adopted
by later generations. Cauchy did the most systematic pioneering work on
definite integral and defined definite integral as the “limit” of sum. Before the
operation of definite integral, he pointed out the existence of integral must
be established. He first proved the basic theorem of calculus strictly using
the mean value theorem. Through the hard work of Cauchy and later Weierstrass, the basic concepts of mathematical analysis were strictly discussed.
He ended the confusion of calculus in the past two hundred years, liberated
calculus and its popularization from the complete dependence on geometric
concept, motion and intuitive understanding, and made calculus develop
into the most basic and largest mathematics subject in modern mathematics.
Cauchy’s research in other areas is also very rich. The theory of calculus of
complex function was founded by him. In algebra, theoretical physics, optics,
and elasticity, he also made outstanding contributions. Cauchy’s achievements in mathematics are not only brilliant, but also astonishing. There are
27 volumes of Cauchy’s complete works and more than 800 works. In the
history of mathematics, Cauchy is the second most prolific mathematician
after Euler. His glorious name, together with many theorems and rules, are
remembered in many textbooks today. As a scholar, he has a quick thinking
and outstanding achievements. From his great works and achievements, it is
not difficult to imagine how he worked diligently all his life (Fig. 8.16).
Fig. 8.16 Cauchy (1789–1857)
599
inequality to describe the limit process. Nowadays, all calculus textbooks still
use the definitions of limit, continuity, derivative, convergence, which were
put forward by Cauchy et al. His explanation of calculus was widely adopted
by later generations. Cauchy did the most systematic pioneering work on
definite integral and defined definite integral as the “limit” of sum. Before the
operation of definite integral, he pointed out the existence of integral must
be established. He first proved the basic theorem of calculus strictly using
the mean value theorem. Through the hard work of Cauchy and later Weierstrass, the basic concepts of mathematical analysis were strictly discussed.
He ended the confusion of calculus in the past two hundred years, liberated
calculus and its popularization from the complete dependence on geometric
concept, motion and intuitive understanding, and made calculus develop
into the most basic and largest mathematics subject in modern mathematics.
Cauchy’s research in other areas is also very rich. The theory of calculus of
complex function was founded by him. In algebra, theoretical physics, optics,
and elasticity, he also made outstanding contributions. Cauchy’s achievements in mathematics are not only brilliant, but also astonishing. There are
27 volumes of Cauchy’s complete works and more than 800 works. In the
history of mathematics, Cauchy is the second most prolific mathematician
after Euler. His glorious name, together with many theorems and rules, are
remembered in many textbooks today. As a scholar, he has a quick thinking
and outstanding achievements. From his great works and achievements, it is
not difficult to imagine how he worked diligently all his life (Fig. 8.16).
Fig. 8.16 Cauchy (1789–1857)