math

The amount of apples can be represented by a number $1,2,3\ldots$. The length and time can also be represented by decimal/real numbers $1.3, \pi, 3,\ldots$. The phase of an electric circuit can be represented by complex numbers! In this sense, physics is useful by abstracting away our world into the world of math. Beyond numbers, another mathematical object is used to represent things like velocity and position. This is the humble vector, an object with both magnitude and direction....

Unit Conversions 1 meter = 100 millimeters = 3.281 feet = 39.37 inches. This is an example of unit conversion. Sometimes, unit conversion is used to convert quantities from an unfamiliar unit to a familiar one. Currently, 1 US Dollar is equivalent to 151 Japanese Yen1 2. At times, the change of unit is for clarity, to express quantities of large or small amounts into comprehensible numbers. For instance, instead of several thousand steps, I find the unit of several miles3 more graspable....

I was watching a youtube video 1. The video was about the speed of light in a medium and I think it would intresting to do some relaxing programming with Julia. Specifically, I would like simulate some light propogating media with varying dielectric. This post will go with the following steps. Derive the equations from Maxwell’s equation in a dielectric. Simulate the wave equations. Explore! From Maxwell’s Equations Here are Maxwell’s Equations known in a dielectric in general3....

Tests are one of those necessary evils in the world. A good test does what the name implies, it tests the knowledge of the person. Usually this is down to asses progress in a class or for self learning. Though sometimes this could go wrong (or right, keep reading). For essay and long form questions, there is a spectrum of right or wrong. In math and physics and science in general, the dreaded word problem can present many logical traps and common misconception traps....