Partial Differential Equations · Calculus
The Heat Equation
The heat equation models diffusion. Fourier series assemble the solution on a finite interval; the Gaussian heat kernel solves it on the real line.
WHAT STUDENTS WILL LEARN
✓Derive the heat equation from physical principles
✓Solve on a finite interval using separation of variables
✓Solve on the real line using the heat kernel
✓Analyze long-time behavior and the maximum principle
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