#vectors

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

In this video I prove formulas 2 and 3 of the differentiation rules for vector functions and show that the derivative of a vector function multiplied by a real-valued function has the same result as the

In this video I go over Formula 1 of the differentiation rules for vector functions and show the derivative of the addition (or subtraction) of vector functions is just the derivative of each vector function

In this video I go over Formula 1 of the differentiation rules for vector functions and show the derivative of the addition (or subtraction) of vector functions is just the derivative of each vector function

In this video I show that the derivative or tangent vector of a curve defined by a vector function always points in the direction in which the parameter t is increasing. I show this by analyzing how the

Exercise 1: Tangent Vector Points in the Direction of Increasing t In this video I show that the derivative or tangent vector of a curve defined by a vector function always points in the direction in which