1. ### Mathematica Solving 2-D partial integro-differential equation

While reproducing a research paper, I came across the following equation, ∂f/∂t−(H(f)(∂f/∂x)=0 where [H(f)] is hilbert transform of 'f.' and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is...
2. ### 'Unusual' mathematical step in integration

I'm following a derivation in my lecture notes of total average particle number in an ideal classical gas (statistical physics approach). I follow it to the line (though the specific terms don't matter): \left<N\right> = e^{\mu/\tau} \frac{\pi}{2} \int_0^\infty \left(n \,dn \,e^{- \frac{\hbar^2...
3. ### I Fredholm integral equation with separable kernel

Hi at all On my math methods book, i came across the following Fredholm integ eq with separable ker: 1) φ(x)-4∫sin^2xφ(t)dt = 2x-pi With integral ends(0,pi/2) I do not know how to proceed, for the solution...
4. ### Finding displacement using net work?

Homework Statement The question is: A 2 kg particle is moving in the positive x direction with the speed of 5 m/s. As it passes the origin, a force F = (30 N - 2N/s*t)i is applied to it. Where does the particle come to a stop? Homework Equations F=ma W = integral F(x)dx K=.5mv^2 The Attempt...
5. ### Good texts for solving PDE's by integral transforms

I look for good books on solving partial diffrential equations (PDE's) using integral transforms specially Fourier and laplace transforms. Do you have any recommendations for such books? I don't look for a book concerned with the theory, rather, with the methods itself (a suitable book for a...