# Month: November 2020

## Overview of Gauss’ Theorem and Basics of Integration

It turns out that deriving Gauss’ Law is easier said than done. There are several steps according to a StackExchange post [1]. The first of these steps is understanding Gauss’ Theorem. Hmm. Perhaps Gauss used his own theorem to derive his electrostatics law. After a quick online search, it is clear that Gauss’ Theorem is …

## Gauss’ Law, Part 1

In Derivation #3, the expression, $\frac{\partial \beta(t)}{\partial t}$, was written. This is an expression for a derivative of a function $\beta(t)$. Now that a derivative has been introduced, Maxwell’s equations can be investigated. I start with Gauss’ Law. But first, slightly more information about derivatives is needed. I can consider the pieces of …

## Finite Differences

Here are a few notes about the symbol $\Delta$. This symbol appears frequently in physics. Let $\alpha$ be a real number. This statement is equivalent to $\alpha \in \mathbb{R}$. Then $\Delta \alpha$ can be defined as follows. Definition 1 Define a finite difference as $\Delta \alpha \equiv \alpha_2 – \alpha_1$. …

## Remarks on the Lorentz Transformation and One Question

This is a summary of the second part of Appendix A in Albert Einstein’s book [1]. By second part, I mean the part immediately after the derivation of the Lorentz transformation. If there is no relative motion between the coordinate systems with respect to the $y$ and $z$ axis of $K$, then …

## The Lorentz Transformation

This is an attempt to clarify the brief derivation of the Lorentz transformation in Albert Einstein’s book [1]. Suppose that the speed of light, $c$, is the same regardless of whether a coordinate system is or is not translating with a nonzero speed.Next consider two coordinates systems.The first is called $K$ and the …