
Differential geometry of planar curves
In this blog we explore some basic concepts of the geometry of smooth curves in the plane. A moving point \(p\) is described mathematically by letting \(p\) be a function of time \(t\), so that we can write \[p(t)=(x(t),y(t)).\] The velocity is the first derivative of \(p\) with respect to \(t\), that is \[v(t)=\frac{dp}{dt}(t)=\left(\frac{dx}{dt}(t),\frac{dy}{dt}(t)\right),\] For […]

The damped and forced oscillator
We show how to solve the differential equation for mass on a spring with damping forces and a external periodic force acting on the mass.