Calculus ============ .. figure:: assets/DifferentialANDIntegralOnOnePage.png :align: center LaTeX source of this image is `here `_ . Differential of Functions ------------------------------- Integrals -------------- Sometimes a integral on Real plane can be very hard, one of the techniques is to work on Complex plane and use contour integral. 1. Contours: use Ghost Contours so that we don't need to calculate these complicated integrals. 2. Branch Cut: cuts are needed if we have got branch points on the complex plane. 3. Residue Theorem: we can write down the integral by calculating the residue of the integrand, .. math:: \int_C f(z) \mathrm dz = 2\pi i \sum_j \text{Residue}(f(z_j)), where :math:`z_j` are the poles.