In this first lecture of the course we begin by deriving the heat equation. The purpose of this derivation is to show how partial differential equations can arise naturally to describe physical processes. We derive the heat equation for a one-dimensional rod using the conservation of heat energy, Fourier's Law, and other first-principles. The result is an explicit partial differential equation that we will work to understand and solve in the coming lectures.
Learn more about how the heat equation models chemical pollutants too: https://www.youtube.com/watch?v=V5w5BUSiK7o&t=8s
Lectures series on differential equations: https://www.youtube.com/watch?v=UDUH58w4-5w&list=PLXsDp0z6VWFTkAhFApYsNfqgRvZrPTeom
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
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