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