Re: Problems Using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg117262] Re: Problems Using Mathematica
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Sun, 13 Mar 2011 05:26:20 -0500 (EST)
- References: <ilfi6t$79c$1@smc.vnet.net>
On 12/03/2011 10:34, Crystal wrote:
> Hello Friends,
> I'm almost racking my head against the wall trying to solve this
> problem... maybe because I'm new to Mathematica but there's no point
> trying to learn without help from forums like this.
>
> Here are my problems (I'm hoping the questions should render well in
> Mathematica environment with copy/paste):
>
> Problem 1
>
> \[Bullet] Consider the following set of equations
>
> {A E^(\[Alpha] Subscript[L, 1]) - C Cos[\[Gamma] Subscript[L, 1]] -
> B Sin[\[Gamma] Subscript[L, 1]] == 0,
> A E^(\[Alpha] Subscript[L, 1]) \[Alpha] -
> B \[Gamma] Cos[\[Gamma] Subscript[L, 1]] +
> C \[Gamma] Sin[\[Gamma] Subscript[L, 1]] ==
> 0, -D E^(-\[Alpha] Subscript[L, 2]) + C Cos[\[Gamma] Subscript[L,
> 2]] +
> B Sin[\[Gamma] Subscript[L, 2]] == 0,
> D E^(-\[Alpha] Subscript[L, 2]) \[Alpha] +
> B \[Gamma] Cos[\[Gamma] Subscript[L, 2]] -
> C \[Gamma] Sin[\[Gamma] Subscript[L, 2]] == 0}
>
> where
>
> \[Alpha]^2 + \[Gamma]^2 == v^2
>
> with given v and
>
> L == -Subscript[L, 1] + Subscript[L, 2]
>
> Derive the eigenvalue equation in terms of \[Gamma] and L with v as
> the parameter.
>
>
>
>
> Problem 2
>
> \[Bullet] Given the reflection amplitude given by
>
> B[z] == -((I E^(-(1/2) I z \[CapitalDelta]\[Beta]) A[0] Sinh[s (L -
> z)]
> \!\(\*SuperscriptBox["\[Kappa]", "*"]\))/(
> s Cosh[L s] + 1/2 I (I g + \[CapitalDelta]\[Beta]) Sinh[L s]))
>
> where
>
> s == Sqrt[-(1/
> 4) (I g + \[CapitalDelta]\[Beta])^2 + \[LeftBracketingBar]\[Kappa]
> \
> \[RightBracketingBar]^2]
>
> the reflection gain is given by
>
> Subscript[G, refl] == \[LeftBracketingBar]B[0]/A[0]\
> [RightBracketingBar]^2
>
> For simplicity, put \[Kappa]=1,L=1 and find the lowest three numerical
> solutions of \[CapitalDelta]\[Beta] and g for infinite gain.
>
> Thanks so much
>
That looks awfully like exercises that someone has set for you to solve!
If there is something specific you don't understand about Mathematica,
why not ask that!
David Bailey
http://www.dbaileyconsultancy.co.uk