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We last left off studying the heat equation in the one-dimensional case of a rod the question is how the temperature distribution along such a rod will tend to change over time and This gave us a nice first example for a partial differential equation It told us that the rate at which the temperature at a given point changes over time Depends on the second derivative of that temperature at that point with respect to space where theres curvature in space theres change in time Here were gonna look at how to solve that equation And actually its a little misleading to refer to all of this as solving an equation The PDE itself only describes one out of three constraints that our temperature function must satisfy If its gonna accurately describe heat flow, it must also satisfy certain boundary conditions Which is something well talk about momentarily and a certain initial condition That is you dont get to choose how it looks at time T equals zero thats part of the problem statement T