5 Calculus
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. Topics discussed in this chapter are ...