Julia Set

Vectorfield and Trajectories

$\sin(z)$

$e^z$

$\sqrt{z}$

Animations

• Archimedes' approximation of $\pi$ (.mov)
• Buffons Needle (.gif)
• Monte Carlo Integration (.mov)
• Rotations are Linear (.gif)
• $(\varepsilon,\delta)$ Continuity (.gif)

Slope field Examples (Desmos)

• $\frac{dy}{dx}=x^2-y$
• $\frac{dy}{dx}=-2y$
• $\frac{dy}{dx}=3y^{\frac{2}{3}}$
• $\frac{dy}{dx}=y(2-y)$
• $\frac{dy}{dx}=-\frac{y}{x}$

Sample Scripts

• What do these scripts do?
• A sample sciript for creating a slopefield (MATLAB)
• Approximating $\pi$ by "dropping" needles (MATLAB)
• Complex Function Plotter (Python)
• Using 4th order Runge Kutta to solve an ODE (Python)
• A script to generate Julia sets (Python)
• A Monte Carlo Integration example (Python)
• Low pass filter via FFT (Python)