Physically Interesting Differential Equations 1: The Newton Pendulum

Welcome to the first of a series of articles dedicated to exploring physically interesting differential equations. In most physics students’ minds unfortunately, differential equations are just labeled as ‘that maths tool I might need one day’, resulting in a general attitude of indifference and perhaps mild annoyance. I hope through this series of articles on […]

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 […]