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alexkritchevsky.com | ||
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www.jeremykun.com
Last time we investigated the naive (which I'll henceforth call "classical") notion of the Fourier transform and its inverse. While the development wasn't quite rigorous, we nevertheless discovered elegant formulas and interesting properties that proved useful in at least solving differential equations. Of course, we wouldn't be following this trail of mathematics if it didn't result in some worthwhile applications to programming. While we'll get there eventually, this primer will take us deeper down the rabbit hole of abstraction. |
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terrytao.wordpress.com
A key theme in real analysis is that of studying general functions $latex {f: X \rightarrow {\bf R}}&fg=000000$ or $latex {f: X \rightarrow {\bf C}}&fg=000000$ by first approximating them b |
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thenumb.at
Or, where does that \(\sin\theta\) come from? Integrating functions over spheres is a ubiquitous task in graphicsand a common source of confusion for beginners. In particular, understanding why integration in spherical coordinates requires multiplying by \(\sin\theta\) takes some thought. The Confusion So, we want to integrate a function \(f\) over the unit sphere. For simplicity, lets assume \(f = 1\). Integrating \(1\) over any surface computes the area of that surface: for a unit sphere, we should end... |
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pixiecatsupreme.com
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