Definition talk:Piecewise Continuously Differentiable Function

Other definitions of piecewise continuously differentiable
1. I have searched the list at http://www.proofwiki.org/wiki/ProofWiki:Community_Portal#Wikis_and_Encyclopedias for other definitions of "piecewise continuously differentiable" and found none.

2. I have found these on the Internet (I have done only a limited search):

- Methods of Mathematical Physics, Differential Equations, Richard Courant,D. Hilbert:

(2) is replaced by: The derivative of f is a piecewise continuous function.

3. I have searched the list at http://www.proofwiki.org/wiki/ProofWiki:Community_Portal#Wikis_and_Encyclopedias for other definitions of "piecewise continuously differentiable" by searching for "piecewise smooth", which is sometimes synonymous with "piecewise continuously differentiable" and found:

- scholarpedia.org:

[xi−1..xi] in (2) replaced by (xi−1..xi).

- planetmath.org:

(This seems not to be a different definition, only a reformulation).

4. I have found these on the Internet (I have done only a limited search):

Tyn Myint-U and Lokenath Debnath: Linear Partial Differential Equations for Scientists and Engineers (2007):

- (1) is replaced by: f is piecewise continuous,

- [xi−1..xi] in (2) is replaced by (xi−1..xi),

- included in (2): the one-sided limits f'(xi-1+) and f'(xi-) exist for every i∈{1,…,n}.