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 Incoming links: Differentiation on an exponential-polynomial space

Past exam of the mathematical methods I course of the University of Oxford / 2021 resit / 8 / c / i / Solution 2026-10-25

Write the ordered basis as

B = (1, t, e^{t}, t e^{t})

. Differentiation gives

F (1) = 0, F (t) = 1, F (e^{t}) = e^{t}, F (t e^{t}) = e^{t} + t e^{t} .

The corresponding coordinate vectors form the columns of the representing matrix:

[F]_{B} = M = 0000100000100011 .

This is an example of differentiation on an exponential-polynomial space.

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