121–130 of 214 posts
> Fourier argued that the distribution of heat through the rod could be written as a sum of simple waves. How do you even begin to think of such things? Some people are wired differently.
> Fourier argued that the distribution of heat through the rod could be written as a sum of simple waves. How do you even begin to think of such things? Some people are wired differently.
I think he was very familiar with differential equations and series expansions and the "wild west" stage of calculus in general. The frontier of cool and interesting mathematics has moved a lot in 200 years.
A common mistake I see in people reading mathematics (or even computer science papers) is to think the proof set out in the paper is the thought process that lead to the interesting insight. It is almost always an ex post facto formalisation.
IANAMathematician, but I've tried to come up with a metaphor which I hope isn't too wrong: 1. You've start with a signal fluctuating going up and down, and it's on a strip of little LEDs labeled from -1 to +1. 2. You mount that strip to a motor, and spin it at a certain rate. After a while the afterimages make a blob-shape. 3. For each rotation rate, measure how much the shape appears off-center. In this way you can…
If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.
When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)
If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.
When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)
If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.
Earlier quoted context omitted.
When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)
Did you make sproingies from the tear-off side strips of the printer paper, though? That was the best bit. :P