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1. Complex integral via complex contour

Hi, I am using the Fourier transform to price a European put option. I have obtained the following integral: q(x,\tau)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{e^{-[\omega^2-i\omega(\gamma-3)+2(\gamma-1)]\tau}}{(1-i\omega)(2-iw)}d\omega which I need to solve. I have solved this through...
2. Quartic with complex coefficients

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...
3. Second-order Coupled O.D.E.s with constant coefficients

1. 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...
4. Tricky semi-infinite integral

1. Homework Statement I am trying to integrate \int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp. 2. 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) 3. The Attempt at a Solution I rewrote the problem in terms of the...
5. Help! Two fused semi-infinite rods - hard integral

1. Homework Statement The problem is to find an function that describes the tempurate variation with time and position of an infinitely long heated rod that is made by fusing together two semi infinite rods at x=0. They have perfect thermal contact but are made of two different materials...
6. Heated rod problem

1. Homework Statement I was asked to write the equation that describes the following heated rod: Two rods of different materials that have been fused together on the x-axis at x=0 to form one rod of infinite length. I was thinking of just using the heat equation integrated from...