# Difference between revisions of "Errata: In equation (5.5), the upper limit of the integral should be t"

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<!-- This is a template page for creating an erratum. You should include this page using the subst: operator --> | <!-- This is a template page for creating an erratum. You should include this page using the subst: operator --> | ||

{{errata page | {{errata page | ||

− | | chapter = | + | | chapter = 5 |

− | | page = | + | | page = 135 |

− | | line = | + | | line = 12 |

− | | contributor = < | + | | contributor = E. Tuna |

− | + | | date = 5 Apr 08 | |

− | + | | version = First printing | |

− | + | | text = | |

+ | In equation (5.5), the upper limit on the integral should be <math>t</math> instead of <amsmath>\infty</amsmath>: | ||

+ | <center><amsmath> | ||

+ | y(t)=\int_0^{\boldmath t} H'(t-\tau)u(\tau)d\tau. | ||

+ | </amsmath></center> | ||

+ | |||

+ | Related to this error, the summation in the previous displayed equation should be modified so that <math>t_n < t</math>, otherwise the sum could include inputs that are beyond the current time <math>t</math>. Hence the displayed equation on lines 5-8 should read | ||

+ | <center><amsmath> | ||

+ | \aligned | ||

+ | y(t) &= H(t-t_0) u(t_0) + H(t-t_1) \bigl( u(t_1) - u(t_0) \bigr) + \cdots \\ | ||

+ | &= \bigl( H(t-t_0) - H(t-t_1) \bigr) u(t_0) + | ||

+ | \bigl( H(t-t_1) - H(t-t_2) \bigr) u(t_1) + \cdots \\ | ||

+ | &= \sum_{n=0}^{\mathbold t_n < t}\infty \bigl(H(t-t_n) - H(t-t_{n+1}) \bigr) u(t_n) \\ | ||

+ | &= \sum_{n=0}^{\mathbold t_n < t} \frac{H(t-t_n) - H(t-t_{n+1})}{t_{n+1}-t_{n}} | ||

+ | u(t_n) \bigl( t_{n+1}-t_{n} \bigr). | ||

+ | \endaligned | ||

+ | </amsmath></center> | ||

}} | }} |

## Revision as of 20:46, 5 April 2008

Return to Errata page |

Location: page 135, line 12

In equation (5.5), the upper limit on the integral should be instead of :

Related to this error, the summation in the previous displayed equation should be modified so that , otherwise the sum could include inputs that are beyond the current time . Hence the displayed equation on lines 5-8 should read

(Contributed by E. Tuna, 5 Apr 08)