# Recent content by hancock.yang@

1. ### This is a asymptotic problem

Homework Statement Find the complete asymptotic expansion of the function \sqrt{1+x^{6}} - x^{3}lnx as x\rightarrow\infty and x\rightarrow0. In each case give the asymptotic sequence in decreasing orders of magnitude. Homework Equations I tried the Taylor Expansion about 0. But I don't...
2. ### Change the integral limit

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...
3. ### Do a integral

Yes. n is any integer
4. ### Do a integral

\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
5. ### Cauchy Integral Formula

Thanks, I have worked it out
6. ### Cauchy Integral Formula

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

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...
8. ### Cauchy Integral Formula

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
9. ### 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
10. ### A pendulum oscillation problem

Thank you for your help. I have already worked it out .
11. ### A pendulum oscillation problem

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...