Scalar and Vector Projections: Formulas and Diagrams https://youtu.be/A_cwD8ck2ps

In this video I go over a quick review of the formulas for the scalar and vector projections of one vector onto another, as well as showing their visual representations.

The Dot Product and its Useful Properties https://youtu.be/-GBGMNRlous

In this video I review the dot product formulas and its useful properties such as finding the angle between vectors and calculating work done on an object by a constant force. 

Vectors and the Geometry of Space: Review of Chapter https://youtu.be/VMKb69uDVt0

In this video I go over the end of chapter review questions covering the Vectors and the Geometry of Space chapter. There are 19 questions in total and serve as a good review on vectors, dot products, cross products, as well as the equations of lines, planes, and their applications. 

Blackbody Radiation Question 2: Planck's Law Approximates Rayleigh-Jeans Law at Large Wavelengths https://youtu.be/p2a4QGnzlm0

In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law, it becomes Rayleigh-Jeans Law. This results in a good approximation for Rayleigh-Jeans Law at large wavelengths since the extra terms of the Taylor series become very small.

Blackbody Radiation Question 1: Limit of Planck's Law is 0 as Wavelength Approaches 0 or ∞ https://youtu.be/8gcdHAhVVG0

In this video I show by using l'Hospital's Rule for indeterminate limits, that Planck's Law for blackbody radiation approaches zero as the wavelength approaches zero or infinity.

Graphing a Hyperboloid of Two Sheets in 3D https://youtu.be/MCSeF52Kn20

In this video I sketch a hyperboloid of two sheets, which is a quadric surface with horizontal traces being hyperbolas while vertical traces are comprised of both hyperbolas and ellipses.