# Finding Minimum Value with Mathematica

1. Feb 4, 2012

### aredy29

∂ω2 = (1-cos2(Δt)e-2γ(t))/(nTtsin2(Δt)e-2γ(t))

n,T are assumed as constants. How can I use Mathematica to find the values of Δ and t that will give the minimum values for ∂ω2 ?

2. Feb 5, 2012

### Bill Simpson

If I use Expand on your function I get

1/(n T t)((E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2)

Without knowing the signs of n and T we can't know the sign of the result and can't know minimum.

Both Csc^2 and Cot^2 go to infinity at multiples of Pi. Depending on what your gamma function is, either the term with Csc or Cot will win the race to infinity and I believe you can determine the minimum by inspection.

3. Feb 5, 2012

### aredy29

What do you mean with sign of n and T ?

4. Feb 5, 2012

### Bill Simpson

If n*T is negative the whole function will be flipped upside down, what was a minimum would be a maximum, etc.

5. Feb 6, 2012

### aredy29

n and T are integers and always positive.

6. Feb 6, 2012

### Bill Simpson

Then I believe, if you can verify the result from Expand, that n and T can be ignored and you focus on

E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2

If E^(2 gamma[t]) can be < 1 when delta t=Pi then the minimum appears to be -Infinity.