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Period: 530 BCE to 300 BCE
Greeks Begin Studying Area
The ancient Greeks studied areas, which was the first use of integral calculus. They did not get very far with it, but it was where the interest began. Ancient Greeks used the method of exhaustion to estimate areas and volumes. -
Period: 1000 to 1500
Middle East and Indian Advancement
Over the course of 500 years, mathematicians from these areas made advancements in area of the parabola, trigonometric equations, and series which were all used in calculus. -
John Wallis- "Arithmetica Infinitorum"
Arithmetically explains how to determine the area beneath curves of the form y=x^k where k is a positive integer. He did so by looking at the limit-sum of the kth powers of the first n positive integers. -
Isaac Newton- Fundamental Theorem of Calculus
Isaac Newton develops his fundamental theorem of calculus. It was originally called infinitesimal calculus. This was a major discovery because it is still used today. This is the main basic way to get anti-derivatives and do integrals with bounds. -
Gottfried Leibniz
Also develops his version of infinitesimal calculus. This leads to an argument between the two over who truly discovered calculus. -
Leonhard Euler- Integrating Factor and General Homogeneous Linear
Euler introduced how to solve differential equations that were first-order ordinary by using the integrating factor. He also developed a general method of solving homogeneous linear ordinary differential equations that had constant coefficients.
