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Integrals
Multivariate delta functions
\[\int \delta({g(\vec{x})}) d\vec{x} = \Sigma_{\text{zeros of} g(\vec{x})} \frac{1}{|\nabla g(\vec{x})|}\] Plug this into your integrand and simplify before evaluating.
Completing the square to integrate
Integrals that Mathematica won’t do
When is it a hyperbolic trig function?
Elliptic integrals
Example: computing an orbital period
Abel transform
Example: projecting onto the sky in the distant observer approximation
Fourier transform conventions
Newton’s shell theorems
Useful variable substitutions
Similarity variables