Uploaded February 2025 | Updated September 2026, 1 week ago
Deriving the Heat Equation
We derive the heat equation, also known as the diffusion equation, which is one of the most fundamental PDE. Instead of using formulas like Fick's law, we derive it from basic physical principles where temperature on a metal rod consists of particles jumping randomly to the left and to the right. It should be reminiscent of savings models from ordinary differential equations, as well as compartmental models.
Savings Model: youtu.be/XIiLpNeGZBk
Chemical Tank Model: youtu.be/3Mn31Xy5Px8
Subscribe to my channel: youtube.com/drpeyam
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Deriving the Heat Equation
We derive the heat equation, also known as the diffusion equation, which is one of the most fundamental PDE. Instead of using formulas like Fick's law, we derive it from basic physical principles where temperature on a metal rod consists of particles jumping randomly to the left and to the right. It should be reminiscent of savings models from ordinary differential equations, as well as compartmental models.
Savings Model: youtu.be/XIiLpNeGZBk
Chemical Tank Model: youtu.be/3Mn31Xy5Px8
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
