The Principiaor just Principia. In it he
presents his theories of motion, gravity,
and mechanics, thus explaining the
bizarre orbits of comets, tides and tidal
variations, the movement of the Earth’s
axis (called precession), and motion of the
Moon. And although he used calculus to
find many of his scientific results, Newton
also explained them using older geomet-
ric methods in the book. After all, calcu-
lus was very new. Perhaps he was the first
scientist-writer to make sure everyone
understood what he was proposing.Why was Gottfried Wilhelm Leibniz
important to calculus?
German philosopher and mathematician
Baron Gottfried Wilhelm Leibniz (1646–
1716) was a contemporary of Isaac New-
ton. He is considered by some to be a for-
gotten mathematician, being overshadowed by Newton, but his contributions to
mathematics were just as important. In addition to many other contributions, he
(independently of Newton) developed infinitesimal calculus and was first to describe it
in print. Because his work on calculus was published three years before Isaac New-
ton’s, Leibniz’s system of notation was universally adopted, including the notation for
an integral. In 1684, he published Nova methodus pro maximis et minimis, itemque
tangentibus,a work detailing differential calculus and containing the familiar d(or
d/dx) notation, along with the rules for calculating the derivatives of powers, products,
and quotients.What are the different categoriesof modern calculus?
Modern calculus is divided into numerous types. The following lists just a few of these
categories:
Basic calculus—Basic calculus is the branch of mathematics concerned with limits
and with the differentiation and integration of functions. There is also advanced calcu-
lus,which takes an even more complex view of calculus, with an emphasis on proofs.
Differential calculus—Differential calculus deals with the variation of a function
with respect to changes in the independent variable(s). It does this by determining
212 derivatives and differentials.
Sir Isaac Newton, best known for his laws of motion,
also made important contributions in areas such as
fluid dynamics and celestial mechanics. Library of
Congress.