| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I have a quick question on an example in my book. Mathematical Physics by Butkov, pg. 200 ( concerning Convolution ) All integrals are being evaluated from 0 -> t Integral of ( sin cw * sin c(t-w)dw) = sin ct * integral (sin cw cos cw)dw - cos cw * integral (sin**2 cw)dw = sin ct * ( 1-cos 2ct) / 4c - cos ct * ( 2ct - sin 2ct ) /4c I must be missing something as I can not see the progression. What formula is being used ( 1/2 angle, u * dv , ?? ) thanks, matt
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1526.1 | identities id'd | HOBBLE::GERTLER | Mon Dec 02 1991 12:52 | 12 | |
They've used the expansion of sum/difference of two angles:
sin (ct-cw) = sin(ct) cos(cw) - cos(ct) sin(cw)
in the first step (note: error in your note
>> sin ct * integral (sin cw cos cw)dw - cos cw * integral (sin**2
should be cos ct )
The second step evaluates the integrals using standard closed form
solutions. (Note: in first integral, sin(cw) cos (cw) = 1/2 sin(2cw)
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| 1526.2 | thank you ( book in error ) | 3D::CORKUM | We'll be right there Miss Fletcher | Mon Dec 02 1991 13:00 | 11 |
As you noted....the book had an error...
the second term should not be cos cw INSTEAD it should be cos ct......
It seemed weird to have something related to the integration
variable outside of the integral....
thanks,
matt
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