A quick way to classify stationary points for any $f(x,y)$.

There are several methods of going about classifying the stationary points of a function $f(x,y)$. Here I would like to show a method that I prefer which involves minimal calculation. Let us look at the example of  begin{equation}f(x,y)=2x^3+6xy^2-3y^3-150xend{equation} It should be obvious from the 3D plot above that there are numerous stationary points on our […]

Elementor #457

Table of Contents Being one of the two pillars of modern physics, the theory of relativity is widely recognized. In addition to $E=mc^2$ (which should really be $E=gamma (v) mc^2$) the theory of relativity covers a great range of topics, providing elegant explanations and theories that answer questions from “What is time?” to “What is inside […]

$E=mc^2$, a derivation

$E=mc^2$ is perhaps the most well known equation in the world. First proposed by a patent clerk working in Switzerland in his now world famous (but absolutely unreadable) paper ‘On the Electrodynamics of Moving Bodies’, compiled later by Minkowski, Einstein’s novel idea about how mass and energy are intricately linked and that the classical concept […]

Physically Interesting Differential Equations 2: The Dampened Harmonic Oscillator

Welcome to the second article in the series: Physically Interesting Differential Equations, where we explore fascinating physical systems that can be modeled with differential equations. This week, we shall look at the Poisson equation. The Poisson equation is a class of partial differential equations that are often useful when doing physics of fields. One such example […]

Ch.1 Quadratics

Table of Contents A quadratics equation takes the form [ax^2+bx+c=0] where (a,b,c) are constants, (aneq 0) This equation is interesting because if we were to plot the equation as a function (y) of (x), we get an parabola. The graph, as we shall see, is charateristic of the motion exhibited by an object under the […]

Ch.2 Operations with Nabla Operator

Table of Contents After introducing the mathematical definitions of gradient, divergence, and curl in the last chapter. Let us look at some useful identities that will come in handy when you are actually computing the operations. We will shall also examine two cases where the combination of two operations give a noteworthy result.  Operators We […]