NP-hard by Ciro Santilli 40 Updated 2025-07-16
A problem such that all NP problems can be reduced in polynomial time to it.
Amplifier by Ciro Santilli 40 Updated 2025-07-16
Main implementations: the same as electronic switches: vacuum tubes in the past, and transistors in the second half of the 20th century.
Video 1.
How to make an LM386 audio amplifier circuit by Afrotechmods (2017)
Source. Builds the circuit on a breadboard from minimal components, including one discrete transistor. Then plays music from phone through headset cables into a speaker.
Capacitor by Ciro Santilli 40 Updated 2025-07-16
The fundamental intuition about capacitors is that they never let electrons through.
They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.
Therefore, they cannot conduct direct current long term.
For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.
The key equation that relates Voltage to electric current in the capacitor is:
So if a voltage Heavyside step function is applied what happens is:
  • the capacitor fills up instantly with an infinite current
  • the current then stops instantly
More realistically, one may consider the behavior or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.
Video 1.
Finding capacitance with an oscilloscope by Jacob Watts (2020)
Source. Good experiment.
Diode by Ciro Santilli 40 Updated 2025-07-16
Ideally can be thought of as a one-way ticket gate that only lets electrons go in one direction with zero resistance! Real devices do have imperfections however, so there is some resistance.
First they were made out of vacuum tubes, but later semiconductor diodes were invented and became much more widespread.
Semiconductor diode by Ciro Santilli 40 Updated 2025-07-16
Figure 1. . 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.
Video 1.
Diodes Explained by The Engineering Mindset (2020)
Source. Good video:
NP-intermediate by Ciro Santilli 40 Updated 2025-07-16
This is the most interesting class of problems for BQP as we haven't proven that they are neither:
Pulse width modulation by Ciro Santilli 40 Updated 2025-07-16
GPIO generally only supports discrete outputs.
But for some types of hardware, like LEDs and some motors, the system has some inertia, and if you switch on and off fast enough, you get a result similar to having an intermediate voltage.
So with pulse width modulation we can fake analog output from digital output in a good enough manner.
Jump wire by Ciro Santilli 40 Updated 2025-07-16
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
Video 1.
Making Jumper Wires by PCBurn! (2018)
Source.
Jumper (computing) by Ciro Santilli 40 Updated 2025-07-16
Allows you to connect two adjacent pins of a pin header. Sometimes used as a hardware configuration interface!
Looking at most astronomical object through a telescope is boring because you only see a white ball or point every time. Such targets would likely only be interesting with spectroscopy analysis.
There are however some objects that you can see the structure of even with an amateur telescope, and that makes them very exciting.
Some good ones:
Electronic oscillator by Ciro Santilli 40 Updated 2025-07-16
Something where DC voltage comes in, and a periodic voltage comes out.
Video 1.
Oscillators: RC, LC, Crystal by GreatScott! (2015)
Source. Good video. Contains actual breadboard experiments on oscilloscope and circuit diagrams

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact