Calculus is a set of mathematical
tools for solving certain problems. It assumes the methods of algebra and
geometry, and in turn is used as a starting point for higher forms of
mathematics. Calculus is applied to a wide range of problem in medicine, the
social sciences, economics, biological growth and decay, physics, and
engineering. It is a flexible language for describing physical world: objects
in motion, chemical reactions,
complex surfaces and volumes, heating and cooling, the hard-to-image behaviors
of space and time, and many other events. Not only do all students of medicine,
engineering, physics, biology, and economics study calculus in college, so do
many student of psychology, literature, art, business, and history.
Calculus,
like geometry, is built on a foundation of simple elements that can be drawn on
paper or seen in the mind: curves, slopes, and areas. And if ever a branch of
mathematics was created to deal with real-life problems, this is it. English
physicist Isaac Newton (1642-1727) and German mathematician Gottfied Wilhelm
von Leibniz (1646-1716) invented calculus in the 1600s because it was needed to
solve the cutting edge science and math problems of their time, including how
ti calculate the length of curves, the areas bounded by curves, and the motion
of objects that are accelerating (gaining speed).
More
than three hundred years later, the language of calculus is common to almost
every scientific or technical field. It is essential to the design of engines,
computers, and all other complex machines; to economics, agriculture, and
physics; in fact, to the study of pretty much everything from subatomic
particles to the shape of the Universe. Almost every scientist and engineer in
the world understand at least basic calculus. And even for thore who will never
as adults perform any mathematical operation more complex than bidding on eBay,
the concepts of calculus, like the concepts of basic physics, can
clarify our thinking about the world, make it more effective.
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