Recent content by hancock.yang@

Homework Statement \int^{2\pi}_{0}cos^{2}(\theta)sin^{2}(\theta)cos(\theta)sin(\theta)d\theta If I set x=cos^{2}(\theta), the integral limit should be from 1 to 0 or need I break this integral into to 4 parts (i.e from 1 to 0 plus from 0 to 1 plus from 1 to 0 plus from 0 to 1)? Homework...

Yes. n is any integer

\int^{\pi}_{0}Sin(2Cos(\theta))Cos(2n\theta)d\theta I can apply some software to do this integral. However, I need some procedures for this integral. Any help is welcome

Thanks, I have worked it out

Well,thanks. Could you please give a quick explanation of Cauchy Residue Theorem?

The original problem is this: \oint\frac{(z-a)e^{z}}{(z+a)sinz}dz c=2a centered at z=0 2a<pi we can express the integral around the contour as the sum of the integral around z1 and z2 where the contour is a small circle around each pole. Call these contours C1 around z1 and C2 around z2...

yes. I have done the form like this: \oint\frac{(z-a)e^{z}}{(z+a)}\frac{dz}{sinz} + \oint\frac{(z-a)e^{z}}{sinz}\frac{dz}{(z+a)} however the first one is not the standard Cauchy Integral Formula

Homework Statement Using the Cauchy Integral Formula compute the following integrals,where C is a circle of radius 2a centered at z=o, where 2a<pi Homework Equations \oint\frac{(z-a)e^{z}}{(z+a)sinz} The Attempt at a Solution

Thank you for your help. I have already worked it out .

Homework Statement Consider a pendulum oscillation problem, where pendulum oscillates around the vertical in the downward configuration. Assume that there is no friction at the pivot point around which the pendulum rotates, and assume that there exists a torsional spring that counter acts...