Calculus of Fluxions: * see Endnote 4

from Newton’s Method of Fluxions, written 1671, published 1736; fluxion was his term for the derivative.  The idea was developed during the great Plague of London (1665-67) but only made public years later (after Leibniz published). 

 

Weierstrass:

(1815-1897) German mathematician, father of modern analysis who established the modern theory of functions.  Motivated by a desire to complete the work begun by Abel of Norway and Jacobi of Prussia, primarily Abel’s theorem that the number of independent integrals of algebraic functions is finite and Jacobi’s discovery of multiple periodic functions of many variables.  Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, using the latter to study the properties of continuous functions on closed bounded intervals.

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continuous function:

function for which sufficiently small changes in the input result in arbitrarily small changes in the output; otherwise, a function is said to be a discontinuous function.