Recent content by ab959

OK great thanks I realized this soon after I posted. What I am more interested in knowing is if you classify the roots in terms of the parameters. I.e. knowing when there will be 4 real roots or complex roots etc. My intuition tells me however that if Im(p) not equal to zero then all...

I am trying to solve a fourth order polynomial which is in the following form x^4+Ax^3+(B_1+B_2p)x^2-(C+Ap)x+D+Ep=0 Where A, B_1, B_2, C, D, E, are real parameters and p is a complex parameter. I have investigated many ways of solving this equation however there does not seem to be...

Homework Statement I am trying to solve a system of two coupled ODEs. I am interested in an analytic solution if that is possible. I know it will be messy. \frac{\partial^2 U_1}{\partial x^2}+a_1\frac{\partial U_1}{\partial x^2}+b_1 U_1 = c_1 U_2 \frac{\partial^2 U_2}{\partial...

I ended up just using L'Hopital's rule and it came out quite easily. Thanks Tom you were a lot of help! Very much appreciated.

Hi Tom. As my b is a real number, for the case b=0 this doesn't work. I want to find out the limit as b-> 0 of b * integral. I know that it is equal to zero but I am having proving this. All I really have to do is show that the integral with b=0 is finite. Any suggestions?

Cool. Thanks for the help! It was a very nice step. Here is the solution for anyone interested: \int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp = \frac{\pi e^{tb^2} cos(ibu)}{2|b|}}

Yes I am familiar with it however not in this form. Are you suggesting forming a curve on the complex plane which encloses the points p=+/-ib. The integral over this curve would equal 2*pi*i* Sum of residues?

Homework Statement I am trying to integrate \int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp. Homework Equations I know that \int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} dp= \frac{\pi}{2b}e^{tb^2}erfc(\sqrt{a}x)The Attempt at a Solution I rewrote the problem in terms of the complex...