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17 de abr. de 2024 · Johann Bernoulli (born August 6 [July 27, Old Style], 1667, Basel, Switzerland—died January 1, 1748, Basel) was a major member of the Bernoulli family of Swiss mathematicians. He investigated the then new mathematical calculus , which he applied to the measurement of curves, to differential equations, and to mechanical problems.
3 de may. de 2024 · Bernoulli's formula is sometimes called Faulhaber's formula after Johann Faulhaber who also found remarkable ways to calculate sums of powers. Faulhaber's formula was generalized by V. Guo and J. Zeng to a q-analog. Taylor series. The Bernoulli numbers appear in the Taylor series expansion of many trigonometric functions and hyperbolic functions.
1 de may. de 2024 · The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital, but Leonhard Euler first elaborated the subject, beginning in 1733.
Hace 3 días · Although the rule is often attributed to De l'Hôpital, the theorem was first introduced to him in 1694 by the Swiss mathematician Johann Bernoulli.
25 de abr. de 2024 · 9.3. Bernoulli, Johan (1667-1748) Johann Bernoulli was one of the pioneers in the field of calculus and helped apply the new tool to real problems. His life was one of the most controversial of any mathematician. He was a member of the world's most successful mathematical family, the Bernoullis.
17 de abr. de 2024 · Notable Family Members: brother Johann Bernoulli. Jakob Bernoulli (born January 6, 1655 [December 27, 1654, Old Style], Basel, Switzerland—died August 16, 1705, Basel) was the first of the Bernoulli family of Swiss mathematicians. He introduced the first principles of the calculus of variation.
Hace 5 días · A Bernoulli differential equation is an equation of the form y′ + a(x)y = g(x)yν, y ′ + a ( x) y = g ( x) y ν, where a (x) are g (x) are given functions, and the constant ν is assumed to be any real number other than 0 or 1. Bernoulli equations have no singular solutions.
