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

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</amsmath></center>
 
</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
+
Related to this error, the summation in the previous displayed equation should be modified so that <amsmath>t_n < t</amsmath>, otherwise the sum could include inputs that are beyond the current time <amsmath>t</amsmath>.  Hence the displayed equation on lines 5-8 should read
 
<center><amsmath>
 
<center><amsmath>
 
\aligned
 
\aligned
Line 19: Line 19:
 
     &= \bigl( H(t-t_0) - H(t-t_1) \bigr) u(t_0) +  
 
     &= \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 \\
 
       \bigl( H(t-t_1) - H(t-t_2) \bigr) u(t_1) + \cdots \\
     &= \sum_{n=0}^{\boldmath{t_n < t}}\infty \bigl(H(t-t_n) - H(t-t_{n+1}) \bigr) u(t_n) \\
+
     &= \sum_{n=0}^{\boldmath{t_n < t}} \bigl(H(t-t_n) - H(t-t_{n+1}) \bigr) u(t_n) \\
 
     &= \sum_{n=0}^{\boldmath{t_n < t}} \frac{H(t-t_n) - H(t-t_{n+1})}{t_{n+1}-t_{n}}
 
     &= \sum_{n=0}^{\boldmath{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).
 
       u(t_n) \bigl( t_{n+1}-t_{n} \bigr).

Latest revision as of 17:18, 1 September 2012


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 math, otherwise the sum could include inputs that are beyond the current time math. Hence the displayed equation on lines 5-8 should read

math

(Contributed by E. Tuna, 5 Apr 08)