Recent content by monnapomona

Went to office hours today, it turns out for this question, it wasn't limited to just the residue theorems and Laurent series expansion methods. I tried using Cauchy integral formula, where z0 = 1/2 and f(z) = (z^10 / (z^10 + 2)) and got 2πi / 2049 as the final answer.

Would the poles be z = 1/2, (-2)^(1/10) ?

That's where I'm kind of stuck. For the other function in the denominator, (1/(1+2/z^10)), it doesn't go to 0 even if z = 0?

Not sure if this is correct but would one pole be +1/2 (Used this function (1/(z-(1/2))) for my reasoning)?

Homework Statement Evaluate the integral using any method: ∫C (z10) / (z - (1/2))(z10 + 2), where C : |z| = 1 Homework Equations ∫C f(z) dz = 2πi*(Σki=1 Resp_i f(z) The Attempt at a Solution Rewrote the function as (1/(z-(1/2)))*(1/(1+(2/z^10))). Not sure if Laurent series expansion is the...

Okay, so if it's just the real part, iz+1 = i(x+iy) + 1 = ix - y +1 so the restriction would just be -y+1, where y ≠ 1? I'm unsure what to do for a derivative, in my class notes it states that [log z ]' = 1/z so would it include the whole f(z) function, ie. ((z^2 + 2z + 5) / (iz+1))

Homework Statement Find the largest set D on which f(z) is analytic and find its derivative. (If a branch is not specified, use the principal branch.) f(z) = Log(iz+1) / (z^2+2z+5) Homework EquationsThe Attempt at a Solution Not sure how to even attempt this solutions but I wrote down that...

Homework Statement Describe the set of points determined by the given condition in the complex plane: |z - 1 + i| = 1 Homework Equations |z| = sqrt(x2 + y2) z = x + iy The Attempt at a Solution Tried to put absolute values on every thing by the Triangle inequality |z| - |1| + |i| = |1|...

You would get 1.003003 so its approximately 1. Curious question, why does this approximation matter to the proof or derivation of the original question?

Is dt and dp directly proportional? And I have calculus background from a few years ago so I'm a bit rusty on some concepts... like differentials.

This is where I'm stuck... could i say P2/P1 = P and T2/T1 = T, then take the ln of the equation to bring the exponent down?

I think \gamma = Cp/Cv and R = Cp - Cv. I used an entropy equation and made it equal to 0: 0 = Cp*ln(T2/T1) - R*ln(p2/p1) and got (R/Cp)*ln(p2/p1) = ln(T2/T1). So I solved for R/Cv = \gamma -1 / \gamma... and the final result was (P2/P1)^((\gamma -1) / \gamma) = T2/T1 Am I on the right...

Homework Statement Show that \frac{dp}{p} =\frac{\gamma}{\gamma-1}\frac{dT}{T} if the decrease in pressure is due to an adiabatic expansion.Homework Equations Poisson equations: Pv^{\gamma} Tv^{\gamma - 1} Ideal Gas Law: Pv=R_{d}T, where R_{d} is the dry air gas constant. Hydrostatic...

Say what! Haha awesome. Ah, I got that one! Thanks! :P

Yeah, that's what I was thinking cause if the XC is 0 then we would have to be dividing over 0 to get f since XC = 1/(2πf*C)... is that what you did?