### Fluxions and Calculus

Newton’s first major contribution to our world was his original work
in mathematical fluxions. He worked in mathematics his entire career; his work
in fluxions was the basis for later development. He had this to say: “I
invented the method of series and fluxions in the year 1665, improved them in
the year 1666, and I still have in my custody several mathematical papers written
in the year 1664, 1665, 1666, some of which happen to be dated” (as cited
in North, 1967, p. 11). The method of fluxions was used in mathematical problems
dealing with quantities that changed (or “flowed” as Newton often
said) continuously. Newton developed his methods in connection with some problems
in geometry – such as the problem of determining tangents to curved lines
and the problem of finding the area bounded by a curve.

Click here!

http://webug.physics.uiuc.edu/courses/phys150/spring01/slides/08/newton/sld004.htm

The subject grew into what is now known as differential and integral calculus
(Westfall, 1993).Based on his earlier work in fluxions, was development of calculus.
“One of the greatest contributions to modern mathematics, science, and
engineering was the invention of calculus near the end of the 17th century,”
says The New Book of Popular Science (Grolier, 2000). Without the invention
of calculus, many technological accomplishments, such as landing on the moon,
would have very been difficult. Isaac Newton discovered the Binomial Theorem.
He then formulated the principles of differential calculus. These principles
could be used to express velocities and accelerations (which are simple rates
of change of velocities with time). It was thus if very great value in physics,
as Newton was to demonstrate (Goldstein, Hill, & Lay, 1999).

Newton's method

www.math.carleton.ca/~amingare/ calculus/newton.html

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