ghazi
  • ghazi
somebody please explain unit step function ...how come it is defined at zero...though there is a jump ...but still were are able to differentiate and integrate it from zero ....
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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experimentX
  • experimentX
there are not really called functions ... rather generalized function and derivatives are called generalized derivatives.
ghazi
  • ghazi
it would be great if you could make that generalisation more lucid...actually i am stuck and thinking of finding it other way..
experimentX
  • experimentX
|dw:1346491565254:dw| this is your step function f(t) = u(t-t_0)

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experimentX
  • experimentX
the derivative at t=t_0, would be delta(t-t_0)
ghazi
  • ghazi
|dw:1346491624874:dw|
experimentX
  • experimentX
yeah ... that works as a switch.
ghazi
  • ghazi
how you define derivative at 0?
ghazi
  • ghazi
exactly that works as a switch with constant supply
experimentX
  • experimentX
at 0, the derivative will be equal to ... value of jump times delta(t)
ghazi
  • ghazi
well don't we count for jump..i mean definition of derivative
experimentX
  • experimentX
at this particular case ... you jump is just 1
experimentX
  • experimentX
http://en.wikipedia.org/wiki/Dirac_delta_function
experimentX
  • experimentX
your slope is infinite ... so this acts as inpulse. there a very nice course from mit ocw. particularly exercise.
ghazi
  • ghazi
slope is zero i guess
ghazi
  • ghazi
it's a horizontal line
experimentX
  • experimentX
at zero ... you have infinite slope
ghazi
  • ghazi
impulse function has infinite slope at zero....actually point of confusion arises when i apply this concept in electrical circuit how come they consider derivative at zero or may be i am not able to correlate that properly
experimentX
  • experimentX
working with Green's functions?
ghazi
  • ghazi
no..working with impulse ramp and unit step function....i feel contradictory
experimentX
  • experimentX
http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/step-and-delta-functions-integrals-and-generalized-derivatives/
ghazi
  • ghazi
okay ...i'll have to check this out
experimentX
  • experimentX
don't miss exercise.
ghazi
  • ghazi
sure !! thank you ...

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