Calculus
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.. figure:: assets/DifferentialANDIntegralOnOnePage.png
:align: center
LaTeX source of this image is `here `_ .
Differential of Functions
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Integrals
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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.