Physically Interesting Differential Equations 1: The Newton Pendulum

The picture is quite pretty, but let us try and make sense of it. The vectors point towards the direction of motion, imagine if you are standing on a point in the graph, your motion will follow the direction of the vector, as if you are flowing in a river. The x-axis represents \(\theta\) and […]

Equations of the Weeks Archive 2020

Week 1 March 20th 2020 \[\frac{d^2\psi}{dx^2}+\frac{8\pi^2m}{h^2}[E-U(x)]\psi (x)=0\] We start off strong with the one dimensional \(\text{Schr}\ddot{o}\text{dinger Equation}\). An important equation for all of quantum mechanics, well at least in 1-dimension. Week 2 March 30th 2020 \[P(A|B)=\frac{P(B|A)P(A)}{P(B)}\] This week we are taking it back to the fundamentals. The Bayes Theorem, arguablly the most rudimentary and important in […]

Neat Integrations: \(\int_{-\infty}^{\infty}e^{-x^2}\), and Fourier Transform of the Gaussian Curve

My physics prof once said to our class: as physicists, the two things we can do are Taylor expand and Fourier Transform. Indeed, not only is the Fourier Transform a beautiful piece of mathematics, but also an indispensible tool in modern physics. Today, let’s examine the Gaussian Function that we all know and love and […]