In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a given point. It is defined as the magnitude of the derivative of the unit tangent vector

In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a given point. It is defined as the magnitude of the derivative of the unit tangent vector

In this video, I show that a curve can be represented by multiple different vector functions, called parameterizations of the curve, and that it is often beneficial to reparameterize a curve as a function

In this video, I show that a curve can be represented by multiple different vector functions, called parameterizations of the curve, and that it is often beneficial to reparameterize a curve as a function

In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative

In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative

In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. I also go over normal, binormal vectors, as well as the TNB frame,