Infinitesimal Calculus

This chapter provides a brief introduction to infinitesimal calculus or differential and integral, known as simply, calculus. Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves) and integral calculus (concerning accumulation of quantities and the areas under and between curves). Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Today, Calculus has widespread uses in science, engineering, and economics. Limits are one tool of calculus that helps to calculate values that would be impossible by other methods. Derivatives are the second tool of calculus. Integral is the third and last tool of calculus.