Simple differential equation question

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Main Question or Discussion Point

If I have:
[tex]\frac{dA(t,z)}{dz}[/tex]

is it possible to convert this to a differential in the form:
[tex]\frac{dI(t,z)}{dz}[/tex]
given that [tex]I(t,z)=|A(t,z)|^2/a[/tex]? (Where [tex]a[/tex] is a constant).

Any advice would help, thanks.
 

Answers and Replies

  • #2
tiny-tim
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hi n0_3sc! :smile:

dI(t,z)/dz would be (2/a) A(t,z).dA(t,z)/dz
 
  • #3
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so there's no complex conjugate anywhere?
 
  • #4
tiny-tim
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now i'm totally confused :redface:

are you saying that A is complex, but I is real? :confused:

(and in any case, I has two copies of A, and A (obviously) only has one)
 
  • #5
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Sorry, A is a complex quantity so |A(t,z)|^2=A(t,z)A*(t,z)

I'm confused about differentiating that.
 
  • #6
tiny-tim
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product rule … A'A* + AA'* :wink:
 
  • #7
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thanks :)
 

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