Desmos

Various Desmos projects I've made. While I can't embed each project here, I provide a link and a description of each project below.

Bessel functions J and Y

Power series plots of the Bessel functions of the first $(J_\alpha)$ and second $(Y_\alpha)$ kind.

Complex Fourier Series Waves

Animated Fourier series as projections of a curve in the complex plane.

Convolutions

Graphical examples of convolutions of two square pulses and two triangular pulses.

Damped-driven oscillator

Resonance graphs for the classical damped-driven oscillator.

Digamma and Euler-Mascheroni

Plots of the reciprocal gamma function, Digamma function, and related functions, as well as calculating the Euler-Mascheroni constant from the Digamma function.

Dipole equipotentials

Equipotential plots for dipole configurations. Examples include two point charges, two infinitely long line charges, and an equilateral triangle configuration of point charges. A distance parameter can be tweaked while keeping the dipole momment constant to show the limit as the charges get arbitrarily close together.

Elastic Collisions by Geometry

Geometric solution in phase space for a collision between two objects. Based on the 3Blue1Brown video

Fibonacci Numbers Extended

A cute little module that extends the Fibonacci sequence and the Lucas numbers to noninteger indices.

Fibonacci Number Generating Functions

A demonstration of different generating functions for the Fibonacci numbers.

Finite Square Well Solution

Graphical solution to the quantum mechanical finite square well.

Fourier Transform Visualized

Based on the 3Blue1Brown video, this showcases the geometric intuition behind the Fourier transform. Included are functions for square waves, sawtooth waves, and triangular waves. The function f(t) can be customized to the user's liking.

Heat Equation Solutions

Animated solutions to the heat equation, based on the 3Blue1Brown video.

Hermite functions and the QHO

Plots of the solutions to the Schrödinger equation for the simple harmonic oscillator.

Legendre Polynomials

Recursively defined Legendre Polynomials with graphs.

Maxwell-Boltzmann distribution

Interactive Maxwell-Boltzmann distribution of speeds for an ideal gas.

Riemann Zeta Function spirals

Riemann Zeta function spirals for all $s$. When $\mathrm{Re}[s] > 1$ the spiral converges to the value of $\zeta(s)$, but when $\mathrm{Re}[s] < 1$, the spiral diverges, yet $\zeta(s)$ is analytically continued.

Riemann Zeta Function Critical Strip spiral

Critical strip spiral plotted for the Riemann Zeta function. The spiral satisfies $\left(x(t), y(t) \right) = \left(\mathrm{Re}[\zeta(\frac{1}{2} + it)], \mathrm{Im}[\zeta(\frac{1}{2} + it)]\right)$

Visualization of Risk in Statistics

Using two standard normal distributions to represent what the truth would look like under the null hypothesis ${\rm H_0}$ vs the alternative hypothesis ${\rm H_a}$, the Type I error risk $\alpha$ and Type II error risk $\beta$ are shown as areas under each distribution. Manipulable parameters are the difference in means of ${\rm H_0}$ and ${\rm H_a}$ and $\alpha$.

Venus Pentagram

A lovely plot of the Pentagram of Venus.