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math121a-f23:october_30_monday [2023/10/29 12:17] pzhou |
math121a-f23:october_30_monday [2023/10/29 12:18] (current) pzhou [Ex 4] |
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$$ P(D) y(t) = \int P(D) G(t; s) g(s) ds = \int \delta(t-s)g(s) ds = g(t). $$ | $$ P(D) y(t) = \int P(D) G(t; s) g(s) ds = \int \delta(t-s)g(s) ds = g(t). $$ | ||
- | ==== Ex 4 ==== | + | ==== Ex 3 ==== |
Consider the domain being $[0, | Consider the domain being $[0, | ||
$$ d/dt y(t) = g(t), \quad g(t)=1_{[1, | $$ d/dt y(t) = g(t), \quad g(t)=1_{[1, |