Ciro Santilli @cirosantilli  40

A solid-state electronic switch and amplifier.

Although transistors were revolutionary, it is fun to note that they were just "way cheaper and more reliable and smaller" versions of exactly the main functions that a vacuum tube could achieve

First watch: Video "Oscillators: RC, LC, Crystal by GreatScott! (2015)"

Unified all previous electro-magnetism theories into one equation.

Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.

The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.

The equations are a system of partial differential equation.

The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:

Due to the conservation of charge however, those input functions have the following restriction:

Also consider the following cases:

The goal of finding $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.

Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:

You should also review the intuitive interpretation of divergence and curl.

Notably used to connect:

You can buy large sets of them in combitation of male/male, male/female, female/female. Male/male is perhaps the most important

These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.

Why would someone ever sell a devboard without them pre-soldered!

Only certain battery voltages exist, because this voltage depends intrinsically on the battery's chemical composition.

learn.sparkfun.com/tutorials/battery-technologies/all (CC BY-SA) has a very good summary list, reordered from lowest to highest voltage:

Bibliography:

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.

Vectors with the index on top such as $x^i$ are the "regular vectors", they are called covariant vectors.

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.

Then a specific metric is involved, sometimes we want to automatically add it to products.

E.g., in a context considering the common Minkowski inner product matrix where the $\eta$ 4x4 matrix and $\mu$ is a vector in ${\mathbb{R}}^4$which leads to the change of sign of some terms.

The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.

In particular, the divergence and the Laplacian can be succinctly expressed in this notation:

In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as $x_0$, $x_1$, $x_2$, ${\partial }_0$, ${\partial }_1$ and ${\partial }_2$ instead of the usual letters $x$, $y$ and $z$.