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What Does It Mean to Solve the Heat Equation PDE? An Introduction with Example Solutions and Graphs
The heat equation partial differential equation (PDE) and its solutions were studied by Joseph Fourier in the early 1800's. But what does it mean for a function (temperature profile) u(t,x) to solve the heat equation? And what does the solution represent? It means that the first partial derivative of u(t,x) with respect to time t is equal to a ...
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