ORIGINATION OF CALCULUS

Anytime I am in my class teaching, students always ask me some questions which says ‘’HOW DOES CALCULUS CAME INTO EXISTENCE?’’, WHO IS/ARE THE FOUNDERS OF CALCULUS? ‘’ HOW COME THE NOTATION s ie long s which suppose to be in English language in mathematics.
My answer towards the questions goes thus: First, I defined calculus for them as: The study of change. Calculus can be traced back to the Moscow papyrus [C.1820BC] in which an Egyptian mathematician successfully calculated the volume of pyramidal frustum.
In Greek, Democritus (infinitesimal theory i.e very small),is the first person recorder to consider seriously the division of objects into infinite numbers of cross-section but somehow, his idea was rejected by zeno of Elea and created paradoxes.
To calculate the area and volume of regions and solids Antiphon and Endoxus brought in ideas which were credited. *Archimedes developed this method but at the end of it, it was considered absolete when Newton came in.
In the 11th century, Ibu al-Haytham(Iraqi) devised a formula for the sum of the fourth powers. He performed an integration in order to find the volume of paraboloid and his result was generalized for the integrals of polynomials. His findings where not to the level of the polynomial of higher order or degree .
Kowa saki (Japanese) came up with his own idea of solving problems in integrals. His works were made absolete by Newton and Leibniz.
Among all the various mathematicians, the work of Newton and Leibniz were highly recognized. They were credited for the invention of modern infinitesimal calculus. They developed the fundamental theorem of calculus
Leibniz developed consistent and useful notations and concepts. Newton was the first to organize the field into one consistent subject and provided the most important application in integral calculus.
Newton came to calculus as part of his investigations in Physics and Geometry. He saw calculus as a metaphysical explanation of change. Newton used mathematics as a methodological tool to explain the physical world.
He developed Fluxionum calculus in attempt to evade the informal use of infinitesimals in his calculations.
Leibniz was polymaths and his intellectual interests and achievement involved metaphysics, law, economics, politics, logic and mathematics. Newton saw the tangent as a ratio but to Leibniz, it is the ratio between ordinates and abscissas.
To me, the founders of calculus if I am to record are Newton and Leibniz. They made calculus to become real.
The Notation S
The notation was done by Leibniz. This symbol is called long S.
NOTE: Newton and Leibniz did not create the same calculus and they did not conceive of modern calculus. They were both involved in the process of creating a mathematical system to deal with variable quantities. For Newton, change was a variable quantity over time and for Leibniz it was the difference ranging over a sequence of infinitely close values.
There was a rift about the invention of calculus between Newton and Leibniz.
When Leibniz visited Newton in England, he saw Newton’s unpublished work. He may have gained access to Newton’s manuscripts. They accused themselves of plagiarism.
This dispute had an effect of separating English speaking mathematicians from those in the continental Europe for many years. But in 1820, due to the efforts of analytical society, Leibniz analytical calculus became accepted in England.
Newton introduced the notation (f) for the derivative of function f. Leibniz introduced the symbol S for the integral and wrote the derivatives of a function, y of the variable x as dy/dx.