In this video, I write the vector equation of acceleration in terms of its unit tangent and unit normal vector components, which is useful when analyzing the motion of a particle along a curve. The unit

In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating the velocity vector. This follows from

In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that

In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that

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 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 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 show that the tangent vector (derivative of a vector function) is orthogonal or perpendicular to a vector of constant length. Geometrically this means that the curve is on the surface of

In this video I go over the six main differentiation rules for vector functions, as well as the 2nd (or higher) derivatives. The rules have their similar counterparts for real valued functions, and I leave

In this video I go over another example on derivatives of vector functions, and this time sketch the tangent vector to a plane curve manually as well as with GeoGebra's 3D graphing calculator. The tangent

In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector

In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit

In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued

In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued