Smooth Function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.
Most of this article is about real-valued functions of one real variable. A discussion of the multivariable case is presented towards the end.
Read more about Smooth Function: Differentiability Classes, Parametric Continuity, Geometric Continuity
Famous quotes containing the words smooth and/or function:
“he changed and ran
Through many shapes; I lunged at the smooth throat
Of a great eel; it changed, and I but smote
A fir-tree roaring in its leafless top;
And thereupon I drew the livid chop
Of a drowned dripping body to my breast....”
—William Butler Yeats (1865–1939)
“The intension of a proposition comprises whatever the proposition entails: and it includes nothing else.... The connotation or intension of a function comprises all that attribution of this predicate to anything entails as also predicable to that thing.”
—Clarence Lewis (1883–1964)