vol 4: Glossary
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Calculus
[Hazewinkel, Calculus] [Borowski, Calculus]
Calculus was invented independently by Isaac Newton ( ) and Gottfried Wilhelm Leibniz ().
The world of calculus is populated by functions and operators. Operators transform functions into other functions. At the bottom level we have functions that are simply constants, like the natural numbers, and the arithmetic operators that operate on these functions to give us ordinary arithmetic, 1 + 1 = 2 and so on.
The operators of calculus are called differentiation and integration. The functions of calculus are all those functions which are either differentiable, integrable, or both. We may see integration as an extension of the idea of addition and differentiation as an extension of subtraction.
The simplest and clearest application is in Newtonian mechanics. The dynamic law in mechanics is written f = ma, or in the language of calculus,
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