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Information on calculus:
Calculus (Latin, calculus, a small stone used for counting)
is a branch of mathematics that includes the study of limits, derivatives,
integrals, and infinite series, and constitutes a major part of modern
university education. Historically, it has been referred to as "the
calculus of infinitesimals", or "infinitesimal calculus".
Most basically, calculus is the study of change, in the same way that
geometry is the study of space.
Calculus has widespread applications in science and engineering
and is used to solve problems for which algebra alone is insufficient.
Calculus builds on algebra, trigonometry, and analytic geometry and includes
two major branches, differential calculus and integral calculus, that
are related by the fundamental theorem of calculus. In more advanced mathematics,
calculus is usually called analysis and is defined as the study of functions.
More generally, calculus (plural calculi) can refer to any method or
system of calculation guided by the symbolic manipulation of expressions.
Some examples of other well-known calculi are propositional calculus,
predicate calculus, relational calculus, and lambda calculus.
While some of the ideas of calculus were developed earlier in Greece,
China, India, Iraq, Persia, and Japan, the modern use of calculus began
in Europe, during the 17th century, when Isaac Newton and Gottfried Wilhelm
Leibniz built on the work of earlier mathematicians to introduce its basic
principles. This work had a strong impact on the development of physics.
Applications of differential calculus include computations involving
velocity and acceleration, the slope of a curve, and optimization. Applications
of integral calculus include computations involving area, volume, arc
length, center of mass, work, and pressure. More advanced applications
include power series and Fourier series. Calculus can be used to compute
the trajectory of a shuttle docking at a space station or the amount of
snow in a driveway.
Calculus is also used to gain a more precise understanding of the nature
of space, time, and motion. For centuries, mathematicians and philosophers
wrestled with paradoxes involving division by zero or sums of infinitely
many numbers. These questions arise in the study of motion and area. The
ancient Greek philosopher Zeno gave several famous examples of such paradoxes.
Calculus provides tools, especially the limit and the infinite series,
which resolve the paradoxes.
