Unformatted text preview: Definition 4.1 . The Dirac delta function at a, δ a ( t ) , is an op-erator that satisﬁes Z ∞ g ( t ) δ a ( t ) dt = g ( a ) for any continuous function g ( t ) . In Physics, if f ( t ) , a ≤ t ≤ b is a force that acts only during a short period of time interval [a, b], the impulse p of force f ( t ) is computed as Z b a f ( t ) dt. δ a ( t ) can be viewed as an instantaneous unit impulse that occurs pre-cisely at the instant t = a. And pδ a ( t ) is an instantaneous p units impulse that occurs precisely at the time t = a. δ a ( t ) is an important function used in modelling real phenomena, for example,...
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- Spring '11
- Derivative, Dirac delta function, Generalized function