Is exp(-ax) a Piecewise Smooth Function?

Thread starter jaejoon89
Start date Apr 14, 2009
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Functions Smooth

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The function exp(-ax), where a is a positive constant, is considered piecewise smooth because it is smooth everywhere, with no points of discontinuity. This aligns with the definition of piecewise smooth, which requires the function to be smooth except at finitely many points. Since exp(-ax) has zero points of non-smoothness, it meets this criterion. Therefore, it can be used to find a Fourier series representation. The discussion confirms that exp(-ax) is indeed piecewise smooth.

Apr 14, 2009

jaejoon89

I'm trying to find a Fourier series for exp(-ax) where a is a positive constant. How is exp(-ax) piecewise smooth?

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Apr 14, 2009

CompuChip

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It is piecewise smooth in one big piece

If you take piecewise smooth to mean: smooth in all but finitely many points, it satisfies the definition because the number of points in which it is not smooth is zero (< \infty).

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