The founder of the great French analytical school of mathematicians of the nineteenth century was Augustin Louis Cauchy (1789-1857).
He taught at irregular intervals and in various places, owing to political circumstances; and his great influence was then exerted chiefly through his many excellent textbooks on higher mathematics.
In the "Cours a"analyse: analyse algébrique" of 1821, Cauchy gave a thoroughly rigorous and modern form of Euler's (q.v.) "Introductio." The strict treatment in it of infinite series has become classical. The breach with Lagrange's (q.v.) ideas, caused by the rigid foundation of the infinitesimal calculus on the not new, but thoroughly reformed, doctrine of limits, first appeared in the "Résumé des leçons . . . sur le calcul infinitésimal" of 1823.
Other books on calculus and its applications to geometry were afterwards published. Cauchy's "Exercices de mathimatiques" are collections of memoirs, in which there is some repetition of original parts of his textbooks.
His work is rather dryly expressed, and he does not always seem conscious of the exact bearing of the important results he discovered — particularly in the theory of functions based on the idea of complex integration.
His influence combined with that of Euler to shape the very important work of Niels Henrik Abel (1802-1829), and with that of Gauss (q.v.) in the work of Dirichlet and Riemann. The work of Cauchy's School proper was carried on by Joseph Liouville (1809-1882); Briot; Bouquet; Charles Hermite (1822-1901); and, in a less original way, by the Abbe Moigno (1804-1884).
1102445989
He taught at irregular intervals and in various places, owing to political circumstances; and his great influence was then exerted chiefly through his many excellent textbooks on higher mathematics.
In the "Cours a"analyse: analyse algébrique" of 1821, Cauchy gave a thoroughly rigorous and modern form of Euler's (q.v.) "Introductio." The strict treatment in it of infinite series has become classical. The breach with Lagrange's (q.v.) ideas, caused by the rigid foundation of the infinitesimal calculus on the not new, but thoroughly reformed, doctrine of limits, first appeared in the "Résumé des leçons . . . sur le calcul infinitésimal" of 1823.
Other books on calculus and its applications to geometry were afterwards published. Cauchy's "Exercices de mathimatiques" are collections of memoirs, in which there is some repetition of original parts of his textbooks.
His work is rather dryly expressed, and he does not always seem conscious of the exact bearing of the important results he discovered — particularly in the theory of functions based on the idea of complex integration.
His influence combined with that of Euler to shape the very important work of Niels Henrik Abel (1802-1829), and with that of Gauss (q.v.) in the work of Dirichlet and Riemann. The work of Cauchy's School proper was carried on by Joseph Liouville (1809-1882); Briot; Bouquet; Charles Hermite (1822-1901); and, in a less original way, by the Abbe Moigno (1804-1884).
COMPLEX INTEGRATION AND CAUCHY'S THEOREM
The founder of the great French analytical school of mathematicians of the nineteenth century was Augustin Louis Cauchy (1789-1857).
He taught at irregular intervals and in various places, owing to political circumstances; and his great influence was then exerted chiefly through his many excellent textbooks on higher mathematics.
In the "Cours a"analyse: analyse algébrique" of 1821, Cauchy gave a thoroughly rigorous and modern form of Euler's (q.v.) "Introductio." The strict treatment in it of infinite series has become classical. The breach with Lagrange's (q.v.) ideas, caused by the rigid foundation of the infinitesimal calculus on the not new, but thoroughly reformed, doctrine of limits, first appeared in the "Résumé des leçons . . . sur le calcul infinitésimal" of 1823.
Other books on calculus and its applications to geometry were afterwards published. Cauchy's "Exercices de mathimatiques" are collections of memoirs, in which there is some repetition of original parts of his textbooks.
His work is rather dryly expressed, and he does not always seem conscious of the exact bearing of the important results he discovered — particularly in the theory of functions based on the idea of complex integration.
His influence combined with that of Euler to shape the very important work of Niels Henrik Abel (1802-1829), and with that of Gauss (q.v.) in the work of Dirichlet and Riemann. The work of Cauchy's School proper was carried on by Joseph Liouville (1809-1882); Briot; Bouquet; Charles Hermite (1822-1901); and, in a less original way, by the Abbe Moigno (1804-1884).
He taught at irregular intervals and in various places, owing to political circumstances; and his great influence was then exerted chiefly through his many excellent textbooks on higher mathematics.
In the "Cours a"analyse: analyse algébrique" of 1821, Cauchy gave a thoroughly rigorous and modern form of Euler's (q.v.) "Introductio." The strict treatment in it of infinite series has become classical. The breach with Lagrange's (q.v.) ideas, caused by the rigid foundation of the infinitesimal calculus on the not new, but thoroughly reformed, doctrine of limits, first appeared in the "Résumé des leçons . . . sur le calcul infinitésimal" of 1823.
Other books on calculus and its applications to geometry were afterwards published. Cauchy's "Exercices de mathimatiques" are collections of memoirs, in which there is some repetition of original parts of his textbooks.
His work is rather dryly expressed, and he does not always seem conscious of the exact bearing of the important results he discovered — particularly in the theory of functions based on the idea of complex integration.
His influence combined with that of Euler to shape the very important work of Niels Henrik Abel (1802-1829), and with that of Gauss (q.v.) in the work of Dirichlet and Riemann. The work of Cauchy's School proper was carried on by Joseph Liouville (1809-1882); Briot; Bouquet; Charles Hermite (1822-1901); and, in a less original way, by the Abbe Moigno (1804-1884).
1.99
In Stock
5
1
COMPLEX INTEGRATION AND CAUCHY'S THEOREM
COMPLEX INTEGRATION AND CAUCHY'S THEOREM
Related collections and offers
1.99
In Stock
Product Details
| BN ID: | 2940016329338 |
|---|---|
| Publisher: | OGB |
| Publication date: | 03/18/2013 |
| Series: | Cambridge Tracts in Mathematics and Mathematical Physics , #15 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| File size: | 4 MB |
From the B&N Reads Blog