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Internet Message Format  |  1993-01-02  |  1.3 KB
  1. Path: sparky!uunet!zaphod.mps.ohio-state.edu!moe.ksu.ksu.edu!ux1.cso.uiuc.edu!usenet.ucs.indiana.edu!master.cs.rose-hulman.edu!master.cs.rose-hulman.edu!news
  2. From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
  3. Newsgroups: sci.math
  4. Subject: Re: Lapl. Transf. of Product of Functions
  5. Date: 2 Jan 1993 05:42:11 GMT
  6. Organization: Computer Science Department at Rose-Hulman
  7. Lines: 15
  8. Message-ID: <1i39vjINN9kq@master.cs.rose-hulman.edu>
  9. References: <92366.132439CCB104@psuvm.psu.edu>
  10. Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
  11. NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu
  12.  
  13. In article <92366.132439CCB104@psuvm.psu.edu>  writes:
  14. > Hello!
  15. > Does anyone know what the Laplace transform of a product of functions is,
  16. > please?
  17.  
  18. Because the Laplace transform is just a rotated Fourier transform the phrase
  19. "the transform of the convolution is the product of the transforms" works both  
  20. ways.  In particular if f=g h and F, G, and H are their Laplace transforms,  
  21. then F(s)=1/(2Pi I)Integrate[H(r)G(s-r),{r,c-I Infinity,c+I Infinity}] in  
  22. pseudoMathematica notation, where c is chosen so that the path of integration  
  23. is to the right of all singularities of H.
  24. --
  25. Bradley W. Brock, Department of Mathematics
  26. Rose-Hulman Institute of Technology  | "Resist not evil.... Love your
  27. brock@nextwork.rose-hulman.edu       |  enemies."--Jesus of Nazareth
  28.