Math

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

Some fun with Fresnel integrals.

Separation of variables in spherical coordinates

Solving Laplace equation in spherical coordinates.

Potentials of a split cylindrical shell

Double dipping with conformal maps!

Electric potential of angled plates

An application of conformal maps.

An introduction to conformal maps

A gentle introduction to conformal maps.

Integral of the month: \( \int_{-1}^1\frac{1}{x}\sqrt{\frac{1+x}{1-x}}\log\left(\frac{2 x^2+2x+1}{2x^2-2x+1}\right) dx \)

A crazy-ass integral.

Johnson Noise

A derivation of Johnson noise.

Wiener Khinchin Theorem

A proof of Wiener Khinchin theorem.

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.