Derivation of the brachistochrone curve using variational calculus. Discussing its tautochrone property.

With the least-action-principle and Lagrangian mechanics to Newtonian mechanics.

Part 2 of the Lagrange-Hamilton-series. Summary on how to find minima and maxima of multi-dimensional functions, introducing partial derivatives and the gradient.

Part 1 of the Lagrange-Hamilton-series. Summary on how to find minima and maxima of one-dimensional functions using tangents or derivatives, respectively.

Calculation of the parabolic mirror equation.

Calculating the arc length formula in cartesian coordinates in two dimensions.

An analytical solution of the Navier-Stokes equations for a highly simplified flow problem