Hi fellow Hiveians, Today I wanted to complain a little bit about more and more services. The Spread Vector Sadly, one of the things that we have not a lot of control over these days is the spread. What

In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the

In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the

In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. YouTube - Summary - Notes - Playlist - Vector

In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. The TNB Frame is named after the Tangent,

In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. YouTube - Summary - Notes - Playlist - Vector Functions playlist

In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. Since the unit tangent vector is a constant-length one, its

In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. YouTube - Summary

In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. The magnitude

In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two derivatives of the vector function. I derive this using the fact

In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two derivatives of the vector function. I derive this using the fact

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,

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. The arc length for a space curve is calculated in much the same way

In this video I prove Formula 5 of the differentiation rules for vector functions, and this time derive the derivative of the cross product of two vector functions. I solve this by taking the derivative