The Heat Equation in Higher Dimensions - Partial Differential Equations | Lecture 4

The heat equation can be formulated in any number of spatial dimensions, potentially representing heat flow on a surface or through a three-dimensional object. In this lecture we provide the general formulation of the heat equation and discuss how it extends the one we have already seen in one spatial dimension. We discuss initial and boundary conditions, as well as observe that equilibrium temperature distributions now solve partial differential equations of their own. This leads to an introduction of other important PDEs, the Poisson and Laplace equations, which will be featured later on in this lecture series.
Learn more about how the heat equation models chemical pollutants too: • Modelling Diffusion - ...
Lectures series on differential equations: • Welcome - Ordinary Dif...
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