Recent content by redshift

1. Need help understanding problem about Young's double slit

"In Young's double slit experiment, assuming the distance between the slits is 0.07mm and the wavelength of light used is 600 nm, when the screen is 70 cm away, what kind of interference is there." I'm not sure what I'm being asked to determine here. Plugging in the figures into the...
2. Need hint on 'simple' differentiation problem

I need to differentiate z = artan(y/x) with respect to x. Somehow z' = y/(1 +(1/x)^2) doesn't seem right.
3. Cauchy integral problem: can this answer be simplified further?

The question calls for using Cauchy's integral formula to compute the integral for Int.c z/[(z-1)(z-3i)] dz, assuming C is the loop |z-1|=3. Taking z = 1 and f(z) = z/(z-3i), I came up with (2pi*i)/(1-3i), which seems like it could be simplified, but I'm not sure how.
4. Partial fraction of integrand

Alright then, so z = (z + i)A + (z - 2i)B, then expanding gives z = z(A + B) + i(A - 2B) Since the LHS has no i, then A - 2B = 0, and likewise, A + B = 1 But...this is going nowhere. Where am I slipping up?
5. Partial fraction of integrand

I need to find the partial fraction expansion of the integrand z/[(z-2i)(z+i)] Just doing 1/(z-2i) + 1/(z+i) results in (2z-i)/(z-2i)(z+i). It seems easy, but I can't figure out what to multiply by to get the correct numerator.

Many thanks!
7. Partial fraction of integrand

As part of finding the integral of z/(z^2 -1), I'm stuck on getting the partial fraction for it. 1/2 [(1/(z-1) - 1/(z+1)] gives 1/(z^2-1). What should I do to get the z in the numerator. Any hints welcome. Regards
8. Complex analysis question

Cauchy integral question The question calls for finding the integral of dz/((z-i)(z+1)) (C:|z-i|=1) I can't figure out how to do this for (C:|z-i|=1). How does this differ from, say, (C: |z|=2) Regards
9. Explanation of path integrals

What exactly does a path integral measure? Is it area between the ends/bounds of the line? Or is it the length of the line? Just started complex analysis and am comletely confused by this.
10. Time difference between two sine waves

I get it. Since 20 degrees = pi/9, moving LHS A to RHS gives sin (-120pi*t + pi/9) = 1 so, -120pi*t + pi/9 = pi/2 and finally t = 7/2160 seconds Many thanks
11. Time difference between two sine waves

"There are two sine waves having a phase difference of 20 degrees. After one reaches its maximum value, how much time will pass until the other reaches its maximum, assuming a frequency of 60 Hz." Should I go about this by assuming... sin(120pi*t) = sin(120pi(t + x) - 20) Any hints...
12. Integral problem: need help landing this

The problem is to find the definite integral of e^2x/(e^x + e^-x) with the limits of 0 and log 2. Finding the integral was easy enough, e^x - log (1 + e^2x) , but how do I plug log 2 into this. Any hints appreciated.
13. Integral of 1/(1 + cosx)^2

Just finished working out the integral of 1/(1 + cosx)^2 as (1/2)(tan(x/2)) + (1/6)(tan (x/2))^3 + C I'm just wondering whether it's possible to use any substitutions to simplify this further. regards
14. Integral of cos^3 theta

I got cos theta - (1/3)cos^3 theta + C Does this look right?
15. Integral of cos^3 theta

Many thanks. I'll give it a shot.