# Difference between revisions of "Piecewise Continuous function"

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− | A piecewise continuous function ''f'' is a function whose domain can be divided into a [[countable]] number of pieces, and the restriction of ''f'' on each piece is a [[continuous function]]. Piecewise continuous functions are interesting because [[Fourier series]] works on such functions. (That is, the resynthesized function from the Fourier analysis is equal to the original function wherever that function was continuous.) | + | A '''piecewise continuous function''' ''f'' is a function whose domain can be divided into a [[countable]] number of pieces, and the restriction of ''f'' on each piece is a [[continuous function]]. Piecewise continuous functions are interesting because [[Fourier series]] works on such functions. (That is, the resynthesized function from the Fourier analysis is equal to the original function wherever that function was continuous.) |

[[category: mathematics]] | [[category: mathematics]] |

## Revision as of 20:26, 13 November 2007

A **piecewise continuous function** *f* is a function whose domain can be divided into a countable number of pieces, and the restriction of *f* on each piece is a continuous function. Piecewise continuous functions are interesting because Fourier series works on such functions. (That is, the resynthesized function from the Fourier analysis is equal to the original function wherever that function was continuous.)