Calculus - unit2

Text 1. Calculus
Calculus (Latin, calculus. a small stone used for counting) is a branch of
mathematics focused on limits, functions, derivatives, integrals and infiniteseries.

This subject constitutes a major part of modem mathematics education. It
has two major branches. differential calculus and integral calculus, which are
related by the fundamental theorem of calculus. Calculus is the study of change,
in the same way that geometry is the study of shape and algebra is the study of
operations and their application to solving equations. A course in calculus is a
gateway to other, more advanced courses in mathematics devoted to the study of
functions and limits. broadly called mathematical analysis. Calculus has
widespread applications in science, economics, and engineering and can solve
many problems for which algebra alone is insufficient .

Historically, calculus was called "the calculus of infinitesimals", or
"infinitesimal calculus". More generally, calculus (plural calculi) refers to any
method or system of calculation guided by the symbolic manipulation of
expressions. Some examples of other well -known calculi are propositional
calculus, variational calculus, lambda calculus. pi calculus, and join calculus.
Isaac Newton developed the use o f calculus in his laws or motion and
gravitation.

The ancient period introduced some of the ideas that led to integral calculus,
but does not seem to have developed these ideas in a rigorous or systematic way.
Calculations of volumes and areas, one goal of integral calculus, can be found in
the Egyptian Moscow papyrus (c. 1820 DC). but the formulas are mere
instructions, with no indication as to method, and some of them are wrong. From
the age o f Greek mathematics, Eudoxus (c. 408- 355 BC) used the method of
exhaustion. which prefigures the concept of the limit, to calculate areas and
volumes, while Archimedes (c. 287- 212 BC} developed this idea further,
inventing heuristics which resemble the methods of integral calculus.