A little history about Calculus
About 1665, while in his young twenties and studying the motion of the moon, Isaac Newton developed a method of finding areas under a curve. His method of ÒfluxionsÓ and ÒfluentsÓ dealt with ratios of ÒinfinitesimalÓ small pieces, using concepts of limits. These concepts (which Newton viewed from a geometric point of view) were the basic ideas of calculus. Shortly afterwards, in Germany, Gottfried Leibniz worked on similar concepts of ratios of infinitesimals, and their applications.
The concepts had immediate applications. Newton postulated the existence of a force (gravity) acting on objects via an inverse square law; using integral calculus, mathematicians (physicists) were able to then mathematically explain the orbits of the moon and planets. Using integral calculus, mathematicians could compute the distance traveled by an object, given its velocity or acceleration.
By reversing the concepts, and developing differential calculus, scientists could find the tangent to a given curve and maximize or minimize a given function.
Differential and integral calculus were used in find the length of a given curve; these concepts were then used in building accurate pendulum clocks. Within the next century, most areas of science would involve this new method of computation, often called Òthe calculus.Ó
For a general introduction into the history of calculus, see
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html
A major problem of the 1600s was the very important longitude problem, essential to seafaring. The longitude problem could be solved by an understanding of the position of the moon and by creating better clocks. Both these attacks required calculus. Check out the following link for a summary of the longitude problem http://itotd.com/articles/532/the-longitude-problem/
Other interesting links:
A timeline of calculus
http://www.mhhe.com/math/calc/smithminton2e/cd/tools/timeline/
WikipediaÕs entry on calculus
http://en.wikipedia.org/wiki/Calculus