Abstract This paper explains that Daniel Bernoulli used his analytical skills across a broad range of scientific disciplines including probability, hydrodynamics, the flow of blood and blood pressure and Riccati's differential equations. The author points out that Daniel Bernoulli improved mathematical physics with his recognition of many of Newton's theories and his utilization of the more powerful calculus of Leibniz. The paper relates that Bernoulli's mathematical explanation of the behavior of gas led to Boyle's law.
Table of Contents
Introduction
Bernoulli's Contributions to Mathematics
Effect of Bernoulli's Work on Today's World
From the Paper "Aerodynamics is a subdivision of fluid mechanics that deals with the motion of air and other gaseous fluids, and with the forces acting on bodies in motion relative to such fluids. Some of the examples of aerodynamic actions are: the movement of an aircraft through the air, the wind forces applied on a structure and the working of a windmill. Daniel Bernoulli's principle is the main law dictating the motion of fluids, which links an increase in flow velocity to a decrease in pressure. For instance, for the same quantity of air at the entry to the venturi tube below to flow through the restriction in the middle, the air must accelerate."
Abstract This paper explains that L'Hopital, who lived during the conception of modern calculus, was taught by Bernoulli; the result of this tuition was L'Hopital's "Analyse des Infiniments Petits", which became the French reference book in the calculus for a century. The author points out that L'Hopital's name is guaranteed to survive in the memories of thousands of mathematicians because of the L'Hopital rule, which is useful when dealing with indeterminate forms. The paper relates that L'Hopital created the template by which all calculus texts would be modeled and measured against for the next three hundred years. Formulas included.
From the Paper "A natural progression from his two first works on the topic of calculus would have been a serious examination of the integral calculus. Indeed, this was a project that L'Hopital was capable of and actually began to write before his death. However, one of his contemporaries-Leibniz-made it known to L'Hopital that he also endeavored to publish a work covering the same hole in written calculus of the time. Apparently, out of respect to the mathematician who made much of his fame possible, L'Hopital abandoned the project."
Tags: derivative, calculus, Bernoulli, indeterminate, text
