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How were these operators created? It's amazing that Mathematicans found so many operations that are applicable for many more areas.


If I remember correctly, Laplace and Fourier transform are similar in concept where we convert from one domain to another. Is there a reason we would use one over the other in graphics? Is there something one provides that the other doesn't?


I'm not quite sure how this second derivative could relate to these examples. What's a simpler way it relates or a concrete example of how the Laplacian is used?