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

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     &= \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).

Revision as of 21:31, 21 December 2010


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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

math

(Contributed by E. Tuna, 5 Apr 08)