590
P. Liu
Fig. 8.8 Euler (1707–1783)
such as ballistics, ship theory, moon motion theory, and so on. Euler wrote
more than 800 books and papers (Fig. 8.8).
8.9 D’Alembert (1717–1783)
Jean Le Rond d’Alembert (1717–1783) is a famous French physicist, mathematician, and astronomer. He was the main pioneer and founder of mathematical analysis. He gave a better definition of limit, but he did not formulate
this expression. Boyle made such a comment: it is impossible for d’Alembert
to express the limit in strict form without getting rid of the influence of traditional geometric methods, but he was almost the only mathematician who
regarded differential as the limit of function at that time.
D’Alembert is one of the few mathematicians who separated convergent
series from divergent series in the eighteenth century, and he also proposed
a method to judge the absolute convergence of series—d’Alembert discriminant method—which is the ratio discriminant method still used now. He
was also the founder of the theory of trigonometric series, and he also made a
great contribution to the emergence of partial differential equations. In 1746,
he published the paper The Study of the Curve Formed by the String Vibration
under Tension, in which he first proposed the wave equation, and proved the
functional relationship in 1750. In 1763, he further discussed the vibration of
non-uniform strings and proposed a generalized wave equation. In addition,
P. Liu
Fig. 8.8 Euler (1707–1783)
such as ballistics, ship theory, moon motion theory, and so on. Euler wrote
more than 800 books and papers (Fig. 8.8).
8.9 D’Alembert (1717–1783)
Jean Le Rond d’Alembert (1717–1783) is a famous French physicist, mathematician, and astronomer. He was the main pioneer and founder of mathematical analysis. He gave a better definition of limit, but he did not formulate
this expression. Boyle made such a comment: it is impossible for d’Alembert
to express the limit in strict form without getting rid of the influence of traditional geometric methods, but he was almost the only mathematician who
regarded differential as the limit of function at that time.
D’Alembert is one of the few mathematicians who separated convergent
series from divergent series in the eighteenth century, and he also proposed
a method to judge the absolute convergence of series—d’Alembert discriminant method—which is the ratio discriminant method still used now. He
was also the founder of the theory of trigonometric series, and he also made a
great contribution to the emergence of partial differential equations. In 1746,
he published the paper The Study of the Curve Formed by the String Vibration
under Tension, in which he first proposed the wave equation, and proved the
functional relationship in 1750. In 1763, he further discussed the vibration of
non-uniform strings and proposed a generalized wave equation. In addition,