Jacob Bernoulli – Life, work and the Bernoulli equation

Bernoulli was born in Switzerland, in a town called Basel. He studied theology, mathematics, and astronomy. Because of his degree in theology, the Church offered him an appointment, but he turned it down. He traveled around Europe, learning about mathematician discoveries. After his return, Bernoulli became a professor at the University of Basel. He taught mechanics. He got married to Judith Stupanus, and then they had two children, a son named Nicolaus and a daughter. In Bernoulli’s family, many were mathematicians and physicists, but none of his children dedicated to science.

In 1687 he became an appointed professor of mathematics at the University of Basel. He stayed in that position for the rest of his life. Jacob started tutoring his brother Johann Bernoulli, and together they studied many different mathematics topics. They were the first to try to understand and apply the theories of Leibniz. Their brotherly relationship started breaking after some years. They challenge each other in print, and after 1697, their relationship was over. Bernoulli died in 1705 and chose a logarithmic spiral to be drawn in his gravestone. He was the chair of mathematics in Basel university until he died, after this unfortunate event his brother Johann took his position for many more years.

Main Work and Studies

Jacob Bernoulli studied the work of many different mathematicians of his time, such as Descartes and worked in different areas. He worked in infinite series and published his law of large numbers in probability theory. “The interpretation of probability as relative-frequency says that if an experiment is repeated a large number of times then the relative frequency with which an event occurs equals the probability of the even” [1]. As a result of his work, he published five papers in infinite series and proved the divergence of some famous series.

Bernoulli studied the exponential series and came up with the exponential interest. Also, he used the separation of variables technique before it even had a name. Bernoulli was the first to use the integral term to talk about the integration process in calculus. In the year 1696, Bernoulli solved this equation below that now is called “the Bernoulli equation” because of him.

y‘ =p(x)y+q(x)y^n

 Finally, after his death, Bernoulli’s work was published in 1713. His work was incomplete at the time he died, but it was a great contribution to the theory of probability.

The Bernoulli equation helps us understand the lift force in an airplane

The Bernoulli Principle helps us understand how planes can fly. Airplane wings have a unique shape. When the air travels through an airplane wing, it creates a pressure differential between the area over the wing and the area under the wing. The high pressure under the wing generates the lift force to raise the plane.