Notes on Mathematics for Engineers (1959) [pdf]

It helps to gain a 30,000 ft view before zooming into all the details:

   Family                Spatial symmetry                 Example
   ------                ----------------                 -------
   Bessel                Cylindrical (r,θ,z)              circular drum, heatpipes, waveguides
   Legendre (Ordinary)   Axisymmetric Spherical (θ)       earth's bulge spinning on its axis
   Associated Legendre   Full 3D Angular Spherical (θ,ϕ)  spherical harmonics
   Laguerre              Radial Spherical (r)             radial pdf of electron in hydrogen atom

There’s a kind of grief that I feel when I think about how, over the last 70 years, engineers have tended to increasingly rely on tech that makes the math knowledge unnecessary.

The beauty of math has played a huge role in the career choices that I’ve made so far. I changed fields at one point because I realized that the math that practitioners used was almost exclusively all baked into CAD tools. I figured that if that was where the applied math lived, then I wanted to write software for a living.

With a lot of the AI tools now (which I use and appreciate daily FWIW), I’m beginning to see that even in math-heavy sub disciplines of software engineering (e.g. robotics), we’re not exempt from this trend.

Would be good if it included linear algebra, probability and stats in details

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What about all the mathematical discoveries Marc Andreessen claims were kept hidden from academia under the guise of national security?

I once had a mentor that was trying to help me write a CPU characterization and being a phd in math every suggestion he proposed involved derivatives. I was like, why would I describe I486 cache misses in terms of differential equations? To this day I still don’t know what he meant.