In this video, I go over the vector version of Isaac Newton's 2nd Law of Motion, which states that if a force F acts on a particle of mass m producing an acceleration a, then F = m a, where F and a are

In this video, I go over the vector version of Isaac Newton's 2nd Law of Motion, which states that if a force F acts on a particle of mass m producing an acceleration a, then F = m a, where F and a are

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 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 an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This follows from my earlier video in which

In this video, I go over an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This follows from my earlier video in which

In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained as the derivative of the velocity. Thus,

In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained as the derivative of the velocity. Thus,

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

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 show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. YouTube - Summary - Notes - Playlist - Vector

In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. I first convert the helix parametric equations

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 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 manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I begin by converting the parametric equations of the trefoil knot into polar

In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed and position of a charged particle, the