Residue Calculus

Integral of the month: \( \int dr \cos r^2 \)

Some fun with Fresnel 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!

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

Four different ways of evaluating this lovely integral!

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

Three different ways of evaluating this lovely integral!

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

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

Integral of the month: \( \int \frac{x^\alpha dx}{x^2- 2 \beta x + 1} \)

An integral with branch cut.