The most disappointing thing about getting my EE degree was when we got to Laplace transforms, we were presented with the integral without any derivation. We immediately focused on using it with constants, exponentials, sin, cos, unit step, polynomials... Then learned to use partial fractions to get the ratio of polynomials into a form to do the reverse transform. And it was useful because it's easy to express a circuit with resistors, inductors, and capacitors directly into the s plane. But just being handed that initial integral like it's unknowable magic makes one lose one's footing in a way.
This series is going a long way to getting that footing back.
Do Legendre transform next. Even postdocs in statmech I've talked to don't have an intuition for how exactly it encodes information between conjugate variables. This is an excellent paper I would love to animate that gives clean intuition: https://www2.ph.ed.ac.uk/~mevans/sp/LT070902.pdf
The most disappointing thing about getting my EE degree was when we got to Laplace transforms, we were presented with the integral without any derivation. We immediately focused on using it with constants, exponentials, sin, cos, unit step, polynomials... Then learned to use partial fractions to get the ratio of polynomials into a form to do the reverse transform. And it was useful because it's easy to express a circuit with resistors, inductors, and capacitors directly into the s plane. But just being handed that initial integral like it's unknowable magic makes one lose one's footing in a way.
This series is going a long way to getting that footing back.
Do Legendre transform next. Even postdocs in statmech I've talked to don't have an intuition for how exactly it encodes information between conjugate variables. This is an excellent paper I would love to animate that gives clean intuition: https://www2.ph.ed.ac.uk/~mevans/sp/LT070902.pdf
++ Good Post, Also, start here Compilation of 100+ Most Asked System Design, ML System Design Case Studies and LLM System Design
https://open.substack.com/pub/naina0405/p/important-compilation-of-most-asked?r=14q3sp&utm_campaign=post&utm_medium=web&showWelcomeOnShare=false
I find it interesting you like old misinformation but reject new fresh ideas.
Who is rejecting new, fresh ideas?
Idea of II Bro, where are you?