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Exercise 20

Avg difficulty 2.5

If ff is a piecewise continuous, exponentially bounded function defined [0,∞)[0, \infty), prove that the Laplace transform of ff, L(f)(s)=F(s)=∫0∞e−stf(t) dt{\mathcal L}(f)(s)= F(s) = \int_0^\infty e^{-st} f(t) \, dt exists.

Judson, The ODE Project, §6.1 The Laplace Transform, Exercise 20

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Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.