Math

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!

The catenary curve with a sliding end

We dive into calculus of variations to calculate the shape of a rope fixed in one end and free to slide on the other.

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

Three different ways of evaluating this lovely integral!

HDD average seek time

We compute the average seek time on an hard disk drive. This will involve a bit of math related to functions of random variables.

Integral of the month: \( \int \frac{ dx}{x^n+ 1} \)

Branch cuts are your friends. You can have fun with them!