Math

Integral of the month: \( \iint_S dt' dt f(t'-t) \)

When the function depends only on the difference of the parameters...

Lagrange Multipliers

A closer look into Lagrange Multipliers with the geometrical interpretation and a few examples.

Stirling approximation for factorial

Stirling's approximation for the factorial function.

Integrating Gaussians like a boss!

This is a deep dive into Gaussian integrals.

Cauchy-Riemann conditions

We derive Cauchy-Riemann conditions in cartesian and polar coordinates.

Integral of the month: \( \oint_{c} \frac{ |dz|}{|z- \beta|^2} \)

Going around a circle!

Dealing with huge and tiny numbers

We sometimes have to deal with very large and very small numbers in the same equation. This post looks into a probability calculation for an event which has very low success rate but repeats many times.

Integral of the month: \( \int dx \frac{\sin^2 x}{x^2} \)

Four different ways of evaluating this lovely integral!