## ghazi 3 years ago 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 ....

1. experimentX

there are not really called functions ... rather generalized function and derivatives are called generalized derivatives.

2. ghazi

it would be great if you could make that generalisation more lucid...actually i am stuck and thinking of finding it other way..

3. experimentX

|dw:1346491565254:dw| this is your step function f(t) = u(t-t_0)

4. experimentX

the derivative at t=t_0, would be delta(t-t_0)

5. ghazi

|dw:1346491624874:dw|

6. experimentX

yeah ... that works as a switch.

7. ghazi

how you define derivative at 0?

8. ghazi

exactly that works as a switch with constant supply

9. experimentX

at 0, the derivative will be equal to ... value of jump times delta(t)

10. ghazi

well don't we count for jump..i mean definition of derivative

11. experimentX

at this particular case ... you jump is just 1

12. experimentX
13. experimentX

your slope is infinite ... so this acts as inpulse. there a very nice course from mit ocw. particularly exercise.

14. ghazi

slope is zero i guess

15. ghazi

it's a horizontal line

16. experimentX

at zero ... you have infinite slope

17. 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

18. experimentX

working with Green's functions?

19. ghazi

no..working with impulse ramp and unit step function....i feel contradictory

20. experimentX
21. ghazi

okay ...i'll have to check this out

22. experimentX

don't miss exercise.

23. ghazi

sure !! thank you ...