Unformatted text preview: ∞ ). f ( t ) is sum of these three products, f ( t ) = ( t 2t + 3)( u ( t )u 2 ( t )) + e t ( u 2 ( t )u 5 ( t )) + 2 t sin( t ) u 5 ( t ) = ( t 2t + 3) u ( t ) + ( e tt 2 + t3) u 2 ( t ) + (2 t sin( t )e t ) u 5 ( t ) . a Example 3.2 . Express f ( t ) = t 2 e t if < t < 3 cos( t ) if 3 ≤ t < 6 2 t if t ≥ 6 as linear combination of step functions. Solution Notice f ( t ) has three diﬀerent expresses over interval [0, 3), [3, 6) and [6, ∞ ), so we need to have two diﬀerence, u ( t )u 3 ( t ) and u 3 ( t )u 5 ( t ) and f ( t ) = t 2 e t ( u ( t )u 3 ( t )) + cos( t )( u 3 ( t )u 6 ( t )) + 2 tu 6 ( t ) = t 2 e t u ( t ) + (cos( t )t 2 e t ) u 3 ( t ) + (2 tcos( t )) u 6 ( t ) . a...
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 Spring '11
 Dr.Han
 Addition, Summation, Linear combination, Berlin UBahn, step functions

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