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Comment by Fixed Point on Why does separation of variable gives the general solution to a PDE

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+1 At the end of part 4, we have a basis for two 1D operators. How do we know that multiplying these two bases (element wise) will give us a basis for the Laplacian in a 2D rectangle? Why don't we need the "cross-terms"? And how is it enough to be a basis for the 2D region?

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