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math121a-f23:october_30_monday

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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]
Line 68: Line 68:
 $$ P(D) y(t) = \int P(D) G(t; s) g(s) ds = \int \delta(t-s)g(s) ds = g(t). $$ $$ P(D) y(t) = \int P(D) G(t; s) g(s) ds = \int \delta(t-s)g(s) ds = g(t). $$
  
-==== Ex ====+==== Ex ====
 Consider the domain being $[0,\infty)$, and we have Consider the domain being $[0,\infty)$, and we have
 $$ d/dt y(t) = g(t), \quad g(t)=1_{[1,2]}(t). y(0) = 0$$ $$ d/dt y(t) = g(t), \quad g(t)=1_{[1,2]}(t). y(0) = 0$$
math121a-f23/october_30_monday.txt · Last modified: 2023/10/29 12:18 by pzhou