In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m a, and his law on universal gravitation. While observing the Danish

In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m a, and his law on universal gravitation. While observing the Danish

In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite sequence of numbers whose terms are each

In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite sequence of numbers whose terms are each

In this video, I rewrite our earlier equations for the tangential and normal components of acceleration to be in terms of the position vector and its derivatives. This simplifies and standardizes the

In this video, I rewrite our earlier equations for the tangential and normal components of acceleration to be in terms of the position vector and its derivatives. This simplifies and standardizes the

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. #math #vectors

In this video, I determine the time a projectile is in the air, the distance it travels, and the speed it impacts the ground after being launched from 10 meters at an angle of 45 degrees and a speed of

In this video, I determine the time a projectile is in the air, the distance it travels, and the speed it impacts the ground after being launched from 10 meters at an angle of 45 degrees and a speed of

In this video, I determine the vector formula for path of a projectile launched at an angle by integrating the acceleration due to gravity acting on it, and then integrating its velocity vector. When the

In this video, I determine the vector formula for path of a projectile launched at an angle by integrating the acceleration due to gravity acting on it, and then integrating its velocity vector. When the

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 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