#vectorfunctions

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

In this video I prove the main properties of vector function limits, namely the addition, constant multiplication, as well as the dot and cross products of their limits. These properties are identical

In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st solution involves assuming the vector exists, and then using the basic definition of

In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st solution involves assuming the vector exists, and then using the basic definition of

In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix. YouTube - Notes - Playlist - Vector Functions

In this video I show that a continuous vector function in 3D forms a curve in space when tracing out the point on the tip of the vector as it moves in time. Note that a continuous vector function means

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component functions. If the limit exists, then so does the limit of each component