Calculus

The calculus has been originated from the Latin word calculus which meant a small stone that is used for counting. In a broader scope, calculus is the term which focuses on the derivatives, functions, limits, infinite series and integrals. Calculus constitutes a major part in the education of the modern mathematics. There are two important branches in calculus which are integral calculus and differential calculus.  These two branches of the calculus are related by the fundamental theorem of calculus. As like geometry being the study of shape and algebra the study of operations calculus is referred to as the study of change. For entering in to other advanced courses in the field of mathematics, calculus is referred to as the gateway which is more devoted to the study of the limits and functions which are mentioned in a broader scope as mathematical analysis. There are widespread applications of calculus in various fields like, engineering, economics, science in order to solve the problem. Calculus throughout was called in various names like infinitesimal calculus or infinitesimals. Any system or the method of calculation which is mastered by the manipulation of the expressions symbolically is referred to as calculus in a generic way. The lambda calculus, propositional calculus, variational calculus, join calculus, pi calculus, and lambda calculus are some other well known calculi.

History of calculus:

Ideas that initiated the concept of integral calculus was found in the ancient period but lacked in developing a systematic and rigorous way. The Egyptian Moscow papyrus in 1820 BC has the goal of the integral calculus with volumes of calculations. But the formulas that are encrypted in here are mere instructions with no definite instruction for implementing it as a method and again some instructions were found to be wrong. The trial and error is suggested by some like the Morris Kline in the Mathematical thought from ancient to modern times, Vol. I. On the other hand, the method of exhaustion has been used by Eudoxus (c. 408-355 BC) from the time of the Greek mathematics. This work prefigures the notion of the limit to the calculate volumes and areas. Heuristics was invented by Archimedes (c. 287−212 BC) which almost resembles the methods that are used in the integral calculus. Liu Hui later in the third century reinvented the method of exhaustion.

Integral calculus:

The study of the definition, application and the properties of the two concepts that are related are referred to as integral calculus. The two related concepts of the integral calculus are the indefinite integral and the definite integral.

Questions:

• What is calculus?
• What is integral calculus?