jaejoon89
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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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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 ([itex]< \infty[/itex]).
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 ([itex]< \infty[/itex]).