Tag Archives: ODE’s

My sister isn’t “irrational”, her utility function just has large interaction terms.

What happens if, instead of doing a linear regression with sums of monomial terms, you do the complete opposite? Instead of regressing the phenomenon against  , you regressed the phenomenon against an explanation like  ? I first thought of this question several years ago whilst living … Continue reading

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A beautiful depiction of a 1-form by Robert Ghrist. You never thought understanding a 1→1-dimensional ODE (or a 1-D vector field) would be so easy! What his drawing makes obvious, is that images of Phase Space wear a totally different meaning … Continue reading

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How to multiply matrices

This is for my homies in math class. Mathematical matrices are blocks of numbers, arrayed in 2-D. (Higher-dimensional arrays are called tensors.) Left “times” right equals target. Each entry in the target is the result of a series of +’s … Continue reading

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Proof that differential equations are real. The shapes the salt is taking at different pitches are combinations of eigenfunctions of the Laplace operator. (The Laplace operator  tells you the flux density of the gradient flow of a many-to-one function ƒ. As eigenvectors … Continue reading

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Laplace Transform

The LaPlace Transform is simpler than I thought. It’s just the continuous version of a power series. Think of a power seriesas mapping a sequence of constants to a function.Well, it does, after all. Then turn the ∑ into a … Continue reading

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