Calculus is the
mathematical 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. It has two major branches,
differential calculus (concerning rates of change and slopes of curves), and
integral calculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the
fundamental theorem of calculus. Both branches make use of the fundamental notions of
convergence of
infinite sequences and
infinite series to a well-defined
limit. Calculus has widespread uses in
science,
economics, and
engineering and can solve many problems that
algebra alone cannot.
Calculus is a major part of modern
mathematics education. 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 historically been called "the calculus of
infinitesimals", or "
infinitesimal calculus". The word "calculus" comes from
Latin (
calculus) and means a small stone used for counting. 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,
calculus of variations,
lambda calculus, and
process calculus.