# contour

1. ### A Partial Differential Equation Mathematical Modelling

Salutations, I have been trying to approach a modelling case about organism propagation which reproducing with velocity $$\alpha$$ spreading randomly according these equations: \frac{du(x,t)}{dt}=k\frac{d^2u}{dx^2} +\alpha u(x,t)\\\ \\ u(x,0)=\delta(x)\\\ \lim\limits_{x \to \pm\infty}...
2. ### Contour Integration: Branch cuts

1. Homework Statement I am supposed to evaluate the contour integral of the positive branch of $z^{-1/2}$ over the following contour: I believe the answer should be 0, by Cauchy's theorem (loop encloses no poles), but my methods of parameterization have led to non-zero answers. 2...