This course explores the fascinating derivation of the heat equation, tracing its roots in thermodynamics to its unexpected applications in finance and other fields. Beginning with the classical heat equation, students will develop an understanding of partial differential equations (PDEs), diffusion models, and boundary conditions. We’ll then leap into modern applications, discovering how this fundamental equation governs stock options in the Black-Scholes model and the spread of information or substances in various domains. By the end of the course, participants will be equipped to apply mathematical methods from physics to solve complex problems in finance, biology, and beyond. Teachers' note - Take this class even if you aren't the most mathematically inclined! We promise there's something for everyone in this course, we will attempt to derive everything from first principles and make it digestible for a wide array of backgrounds.

Everyone knows the world's most famous equation: E=MC^2, but few know exactly what it means and where it comes from. In this class, we will derive E=MC^2 using only basic high school calculus and trigonometry, while also developing a strong intuition for what the formula signifies in physics and the real world.