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Never heard of Oliver Heaveside and his operator despite using Laplace transforms on a regular basis for year. You learn something new every day. Thanks.
by qubex 9y ago
Never heard of Oliver Heaveside and his operator despite using Laplace transforms on a regular basis for year. You learn something new every day. Thanks.
- Cyph0n 9y agoMy diff equations textbook referred to it as the Heaviside operator. In my EE and control classes, it's called the Laplace transform.
- ncmncm 9y agoOther reasons Heaviside is often ignored are that he was a commoner, and he published all his papers in a newspaper. He originated the theory of transmission lines (inventing the loading coils you still see hanging between telephone poles) and atmospheric radio propagation, both often credited to others. See Paul Nahin, "Oliver Heaviside: Sage in Solitude"
- Cyph0n 9y agoNow that's very interesting! According to his wiki page, he reduced Maxwell's equations from 20 equations (in 20 variables) down to the 4 iconic equations we now refer to as Maxwell's equations. Imagine having to learn EM theory with 20 equations... as if current EM theory courses aren't tough enough already! One of his creations, the step function, is also a key part of many proofs and equations in signal processing.
- ncmncm 9y agoIt should be noted that Maxwell's quaternion formulation of the same relations has just two equations. Vector notation won out over quaternions not from elegance or power, but from practical details of working them on paper. Now that we don't, anymore, quaternions are probably the better notation. Somebody should rewrite an E-M and an optics textbook.
- catnaroek 9y agopls, we use tensor calculus and exterior algebra. More, precisely, the electromagnetic tensor is the exterior derivative of the 4-potential.
- kurthr 9y agoExactly, vector calculus is a useful learning tool, but not used in most higher level (e.g. General Rel, plasma physics, etc) or numerical (super computer) physics calculations. Raising and lowering Kartoffel symbols and their covariant derivative forms make manipulating the coordinate transforms possible (4-6 dimensional)... otherwise it would just look like pages of equations. Interestingly, mechanical engineering also deals almost entirely with tensors... and they've developed extremely intuitive visualization tools.
- mkl 9y ago> Interestingly, mechanical engineering also deals almost entirely with tensors... and they've developed extremely intuitive visualization tools. What visualisation tools are you referring to? That sounds interesting.
- kurthr 9y agoSince all 3D stress/strains are tensor quantities (even for purely linear models), MEs project them into principal axes so that you can see their angle and their peak tesnsile/shear stress. https://en.wikipedia.org/wiki/Cauchy_stress_tensor https://en.wikipedia.org/wiki/Cauchy_stress_tensor Look at Mohr's circle: https://en.wikipedia.org/wiki/Mohr%27s_circle https://en.wikipedia.org/wiki/Mohr%27s_circle Within an object the stresses and strains (and principal components) vary as you move through it. That's part of what makes predicting failures and effects of thermal expansion so complex, etc difficult even ignoring nonlinear effects and failure modes (e.g. crack propagation).
- wbl 9y agohttps://en.wikipedia.org/wiki/Christoffel_symbols https://en.wikipedia.org/wiki/Christoffel_symbols is probably what you wanted to say
- empath75 9y agoWhat kind of newspaper publishes scientific papers?
- ncmncm 9y agoI guess Nahin called it a newspaper because it came out on newsprint, folded over, weekly. It would be called a trade rag, these days, if we had those anymore. https://books.google.com/books?id=ehJbAAAAYAAJ&dq=intitle%3AThe%20electrician&pg=PA10-IA3#v=onepage&q&f=false https://books.google.com/books?id=ehJbAAAAYAAJ&dq=intitle%3A...
- emmelaich 9y agoHe's responsible for the form of Maxwell's equations that we use today.