Exercise 3: Approximating Electric Field of Electric Dipoles using Binomial Series https://youtu.be/RSkkBiOjXnw

In this video, I use the binomial series approximation to demonstrate that the electric field (E) of an electric dipole (two equal but opposite charges separated by a small distance) is proportional to 1 over the distance cubed when measured from a far distance. 

#math #physics #science #education #calculus

Exercise 2: Deriving the 1st Order and 3rd Order Optics Formulas https://youtu.be/leZ0QK_n07k

In this video, I derive the first-order and third-order optics formulas by approximating the refraction formula for light using first and third-order Taylor polynomials, respectively.

Magnetic Isopotentials Explain the Faraday Paradox, Stern-Gerlach Experiment, and Atomic Orbitals https://youtu.be/NOG9VOBtpY4

In this video I summarize the very important work of FractalWoman and Michael Snyder on Isopotentials, which are contours of equal magnetic field strength.

Exercise 1: Taylor Derivatives Equal the Function's Derivatives at x = a https://youtu.be/UqWf2PE1OeE

In this video I prove that the derivatives of a Taylor Polynomial are equal to the derivatives of the corresponding function used in the approximation when x = a. This is because any derivative at x = a of any Taylor polynomial cancels out all the terms (since a - a = 0) except the first term, which is just the corresponding derivative of f at x = a.

Example 1: Approximating Cube Root Function by a 2nd Degree Taylor Polynomial https://youtu.be/0616gOyjbyQ

In this video I approximate the cube root function x^(1/3) by using a 2nd degree Taylor polynomial at a = 8. The first step is to obtain the first 2 derivatives of f at x = 8, and then the third derivative to be used for the error estimation.

Approximating Functions by Taylor Polynomials https://youtu.be/woT9NoaFM_Y

In this video, I demonstrate how Taylor polynomials can be used to approximate functions and how to evaluate the accuracy of these approximations by examining the absolute magnitude of the error.