TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.
Those in indices on bottom are called contravariant vectors.
It is possible to change between them by Raising and lowering indices.
The values are different only when the metric signature matrix is different from the identity matrix.
- math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors/3503875#3503875
- math.stackexchange.com/questions/1520832/real-life-examples-for-eigenvalues-eigenvectors
- matheducators.stackexchange.com/questions/520/what-is-a-good-motivation-showcase-for-a-student-for-the-study-of-eigenvalues
I-V curve of a diode
. Source. This image shows well how the diode is only an approximation of the ideal one way device. Notably, there is this non-ideal voltage drop across the device, which can be modelled as constant. It is however an exponential in fact.
Diodes Explained by The Engineering Mindset (2020)
Source. Good video:- youtu.be/Fwj_d3uO5g8?t=153 how it works
- youtu.be/Fwj_d3uO5g8?t=514 applications:
- protection against accidental battery inversion
- rectifiers, notably mentions a diode bridge
It is quite amazing to read through books such as The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), as it makes you notice that earlier CPUs (all before the 70's) were not made with integrated circuits, but rather smaller pieces glued up on PCBs! E.g. the arithmetic logic unit was actually a discrete component at one point.
The reason for this can also be understood quite clearly by reading books such as Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006). The first integrated circuits were just too small for this. It was initially unimaginable that a CPU would fit in a single chip! Even just having a very small number of components on a chip was already revolutionary and enough to kick-start the industry. Just imagine how much money any level of integration saved in those early days for production, e.g. as opposed to manually soldering point-to-point constructions. Also the reliability, size an weight gains were amazing. In particular for military and spacial applications originally.
A briefing on semiconductors by Fairchild Semiconductor (1967)
Source. Uploaded by the Computer History Museum. There is value in tutorials written by early pioneers of the field, this is pure gold.
Shows:
- photomasks
- silicon ingots and wafer processing
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