One hour before this post was out I was frantically watching a few videos on YouTube trying to understand Laplace transforms and was really puzzled why there isn't a 3b1b video about it yet. Thank goodness it's coming.
Thank you for the work animating and making learning differential equations more accessible. Through studying engineering I have been slowly introduced to their beauty and symmetry across all different types of natural phenomena. In my opinion differential equations do not govern things rather they are an idea that humans can use to predict and understand how the mirco relates to the macro and allow us to see things like EM waves that we are unable to see with our own eyes. The complex exponents are fundamental to this study and Laplace is one of the most revolutionary mathematical ideas which made this visualization possible. I look forward to watching it!
Control systems in general would be very hard to design or analyse without the Laplace transform. That is one of the first serious tools young engineering students learn at MIT.
One hour before this post was out I was frantically watching a few videos on YouTube trying to understand Laplace transforms and was really puzzled why there isn't a 3b1b video about it yet. Thank goodness it's coming.
++ 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
Thank you for the work animating and making learning differential equations more accessible. Through studying engineering I have been slowly introduced to their beauty and symmetry across all different types of natural phenomena. In my opinion differential equations do not govern things rather they are an idea that humans can use to predict and understand how the mirco relates to the macro and allow us to see things like EM waves that we are unable to see with our own eyes. The complex exponents are fundamental to this study and Laplace is one of the most revolutionary mathematical ideas which made this visualization possible. I look forward to watching it!
++ 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
Thanks as always for an informative and beautiful video.
One remark: in the general linear ODE, the first term is given as a_n x^n(t), but for the n-th derivative one should have a_n x^{(n)}(t).
Control systems in general would be very hard to design or analyse without the Laplace transform. That is one of the first serious tools young engineering students learn at MIT.
How I'll be spending my next 30 minutes is no longer a mystery. Thanks 3B1B.
Wow, seems fantastic, will surely have a look at it
++ 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
As a Signal Processing major, I get very excited about complex exponentials and the Fourier Transform. Very excited to watch the video