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:

[$x_{i−1},..x_i$] in (2) replaced by ($x_{i−1},..x_i$).

- 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,

- [$x_{i−1},..x_i$] in (2) is replaced by ($x_{i−1},..x_i$),

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