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

From FBSwiki
Jump to: navigation, search
 
Line 1: Line 1:
 
<!-- 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 = <!-- Replace with the (capitalized) chapter name where the error occurs -->
+
| chapter = 5
| page = <!-- Page number of the erratum -->
+
| page = 135
| line = <!-- Line number of the erratum -->
+
| line = 12
| contributor = <!-- Name of the contributorUses initials + last name (R. M. Murray) -->
+
| contributor = E. Tuna
| date = <!-- Date on which the erratum was reported -->
+
| date = 5 Apr 08
| version = <!-- Version in which the erratum occurred (usually 'First printing') -->
+
| version = First printing
| text = <!-- Text for the description of the error and the fix.  This can be multiple lines, but can't include templates -->
+
| 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 math:

math

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

latex: ../../../texk/kpathsea/progname.c:316: remove_dots: Assertion `ret' failed.

(Contributed by E. Tuna, 5 Apr 08)