math – update

blogging & searching for true math …

What is Calculus??…


Actually, I seriously answered this question to myself the first time I lectured My First Calculus course. I remember, I sat down in front of the textbook I had chosen – Calculus, One and Several Variables, Salas – Hille , the best book for engineers I know untill now – and, before reading what they said about it, I finally gave me my own explanation.

Today, I opened the book again and made the same exercise… I have to admit I am a bit proud 😉 of the coincidences of my answer with the authors, and of being able to enjoy this now as much as I did then:

  • Before Calculus: Math was only able to study static phenomena… More than 2500 years ago ancient  Greeks scholars had started proposing questions about motion, tangents, areas, the infinitely small and the infinitely large…
  • After Calculus: Math becomes able to study movement and change – and thus nature – which is in a constant state of “flux”…
  • Infinitesimal Calculus was a novel approach to see reality… The new key paradigm: The idea of Limit
  • Limit is one of the most important concepts in math… But here I would just like to make an innocent analogy, say: The velocity of a body may be captured by a limit process of considering its different positions in time, just like a movie may be captured by a (limit) process of considering its different static pictures in time…
  • After ancient Greek mathematics the development of math was so slow during centuries, due to the lack of communication among scholars, as well as the inadequate mathematical notations of those days…
  • But we must recall, that it was FERMAT (1607-1665) who anticipated the development of Calculus! While investigating a technique for finding the centers of gravity of various plane and solid forms, he developed a method for determining maxima, minima and tangents to various curves! That was essencially equivalent to differenciation! His work on this area was just invaluable later to Newton and Leibniz.
  • It was not untill Algebra was founded by ancient arabs in the 9th century and Analytic Geometry was introduced by Descartes in the 17th century when – independent from each other – Isaac NEWTON (1642-1727) in England and Gottfried LEIBNIZ (1646-1716) in Germany, founded the basis of what we call Calculus today
  • Since then – around 330 years ago – we have changed the way we see the world, and thus we have changed the world we see: New convergences between science and technology began to take shape! The 18th century marked the starting point of the process that would lead to the applications of Calculus to physics, engineering, economy, biology, and practically any other area we can imagine these days, not forgetting communications and entertainment!
  • In short: CALCULUS… “A mathematical system to deal with variable quantities” & “Elementary mathematics enhanced by the limit process”…


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Nice portrait of the French 2010 Fields medallist mathematician  Cécric Villani



Author: Math - Update

Updating Math In Our Mind & Heart!!...

2 thoughts on “What is Calculus??…

  1. What a beautiful article


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